103 results
Search Results
2. A sparse fast Fourier algorithm for real non-negative vectors.
- Author
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Plonka, Gerlind and Wannenwetsch, Katrin
- Subjects
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FOURIER analysis , *ALGORITHMS , *MATHEMATICAL ability , *NUMERICAL analysis , *SPARSE matrices - Abstract
In this paper we propose a new fast Fourier transform to recover a real non-negative signal x ∈ R + N from its discrete Fourier transform x ̂ = F N x ∈ C N . If the signal x appears to have a short support, i.e., vanishes outside a support interval of length m < N , then the algorithm has an arithmetical complexity of only O ( m log m log ( N / m ) ) and requires O ( m log ( N / m ) ) Fourier samples for this computation. In contrast to other approaches there is no a priori knowledge needed about sparsity or support bounds for the vector x . The algorithm automatically recognizes and exploits a possible short support of the vector and falls back to a usual radix-2 FFT algorithm if x has (almost) full support. The numerical stability of the proposed algorithm is shown by numerical examples. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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3. Nonlinear Kaczmarz algorithms and their convergence.
- Author
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Wang, Qifeng, Li, Weiguo, Bao, Wendi, and Gao, Xingqi
- Subjects
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JACOBIAN matrices , *NONLINEAR equations , *ALGORITHMS , *NEWTON-Raphson method , *NUMERICAL analysis - Abstract
This paper proposes a class of randomized Kaczmarz algorithms for obtaining isolated solutions of large-scale well-posed or overdetermined nonlinear systems of equations. This type of algorithm improves the classic Newton method. Each iteration only needs to calculate one row of the Jacobian instead of the entire matrix, which greatly reduces the amount of calculation and storage. Therefore, these algorithms are called matrix-free algorithms. According to the different probability selection patterns of choosing a row of the Jacobian matrix, the nonlinear Kaczmarz (NK) algorithm, the nonlinear randomized Kaczmarz (NRK) algorithm and the nonlinear uniformly randomized Kaczmarz (NURK) algorithm are proposed. In addition, the NURK algorithm is similar to the stochastic gradient descent (SGD) algorithm in nonlinear optimization problems. The only difference is the choice of step size. In the case of noise-free data, theoretical analysis and the results of numerical based on the classical tangential cone conditions show that the algorithms proposed in this paper are superior to the SGD algorithm in terms of iterations and calculation time. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
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4. Efficient simulation of tail probabilities for sums of log-elliptical risks
- Author
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Kortschak, Dominik and Hashorva, Enkelejd
- Subjects
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COMPUTER simulation , *PROBABILITY theory , *ESTIMATION theory , *PERFORMANCE evaluation , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: In the framework of dependent risks it is a crucial task for risk management purposes to quantify the probability that the aggregated risk exceeds some large value . Motivated by Asmussen et al. (2011) [1] in this paper we introduce a modified Asmussen–Kroese estimator for simulation of the rare event that the aggregated risk exceeds . We show that in the framework of log-Gaussian risks our novel estimator has the best possible performance i.e., it has asymptotically vanishing relative error. For the more general class of log-elliptical risks with marginal distributions in the Gumbel max-domain of attraction we propose a modified Rojas-Nandayapa estimator of the rare events of interest, which for specific importance sampling densities has a good logarithmic performance. Our numerical results presented in this paper demonstrate the excellent performance of our novel Asmussen–Kroese algorithm. [Copyright &y& Elsevier]
- Published
- 2013
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5. A note on the two-step matrix splitting iteration for computing PageRank.
- Author
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Wen, Chun, Huang, Ting-Zhu, and Shen, Zhao-Li
- Subjects
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CONVERGENCE insufficiency , *APPLIED mathematics , *DIFFERENTIAL equations , *NUMERICAL analysis , *ALGORITHMS , *PERIODICALS - Abstract
Computing PageRank plays an important part in determining the importance of Web pages. Based on the classical power method and the inner–outer iteration proposed by Gleich et al. (2010), Gu et al. (2015) presented a two-step splitting iteration, i.e., the power-inner–outer (PIO) iteration, for the computation of PageRank. In this paper, we develop a variant of the PIO iteration by applying multi-step power method to combine with the inner–outer iteration. The new method is denoted as the MPIO iteration, its convergence is analyzed in detail. Numerical experiments on several PageRank problems are used to illustrate the effectiveness of the MPIO iteration. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
6. A new algorithm for solving dynamic equations on a time scale.
- Author
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Jafari, H., Haghbin, A., Johnston, S.J., and Baleanu, D.
- Subjects
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ALGORITHMS , *NUMERICAL analysis , *INITIAL value problems , *DIFFERENCE equations , *NONLINEAR functional analysis - Abstract
In this paper, we propose a numerical algorithm to solve a class of dynamic time scale equation which is called the q -difference equation. First, we apply the method for solving initial value problems (IVPs) which contain the first and second order delta derivatives. Illustrative examples show the usefulness of the method. Then we present applications of the method for solving the strongly non-linear damped q -difference equation. The results show that our method is more accurate than the other existing method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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7. A multilevel decoupled method for a mixed Stokes/Darcy model
- Author
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Cai, Mingchao and Mu, Mo
- Subjects
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MATHEMATICAL decoupling , *STOKES equations , *DARCY'S law , *NUMERICAL analysis , *POROUS materials , *ALGORITHMS , *GLOBAL analysis (Mathematics) - Abstract
Abstract: This paper studies decoupled numerical methods for a mixed Stokes/Darcy model for coupling fluid and porous media flows. A two-level algorithm is proposed and analyzed in Mu and Xu (2007) . We generalize the two-level algorithm to a multilevel algorithm in this paper and present numerical analysis on the error estimates for the multilevel algorithm. The multilevel algorithm solves the mixed Stokes/Darcy system by applying efficient legacy code for single model solvers to solve two decoupled Stokes and Darcy subproblems on all the subsequently refined meshes, except for a much smaller global problem only on a very coarse initial mesh. Numerical experiments are conducted for both the two-level and multilevel algorithms to illustrate their effectiveness and efficiency, and validate the related theoretical analysis. [Copyright &y& Elsevier]
- Published
- 2012
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8. Using vector divisions in solving the linear complementarity problem
- Author
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Elfoutayeni, Youssef and Khaladi, Mohamed
- Subjects
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VECTOR analysis , *LINEAR complementarity problem , *PROBLEM solving , *NONLINEAR systems , *APPROXIMATION theory , *NUMERICAL analysis , *ALGORITHMS - Abstract
Abstract: The linear complementarity problem is to find a vector in satisfying , ,, where and are given. In this paper, we use the fact that solving is equivalent to solving the nonlinear equation where is a function from into itself defined by . We build a sequence of smooth functions which is uniformly convergent to the function . We show that, an approximation of the solution of the (when it exists) is obtained by solving for a parameter large enough. Then we give a globally convergent hybrid algorithm which is based on vector divisions and the secant method for solving . We close our paper with some numerical simulations to illustrate our theoretical results, and to show that this method can solve efficiently large-scale linear complementarity problems. [Copyright &y& Elsevier]
- Published
- 2012
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9. Projected gradient iteration for nonlinear operator equation
- Author
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Huang, Wei and Chen, Di-Rong
- Subjects
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ITERATIVE methods (Mathematics) , *NONLINEAR operator equations , *ALGORITHMS , *MATRIX norms , *STOCHASTIC convergence , *MATHEMATICAL sequences , *NUMERICAL analysis , *CONSTRAINED optimization - Abstract
Abstract: In this paper, we use a projected gradient algorithm to solve a nonlinear operator equation with -norm constraint. Gradient iterations with -norm constraints have been studied recently both in the context of inverse problem and of compressed sensing. In this paper, the constrained gradient iteration is implemented via a projected operator. We establish the -norm convergence of sequence constructed by the constrained gradient iteration when . The performance of the method is testified by a numerical example. [Copyright &y& Elsevier]
- Published
- 2011
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10. An inverse problem of identifying the coefficient of first-order in a degenerate parabolic equation
- Author
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Deng, Zui-Cha and Yang, Liu
- Subjects
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INVERSE problems , *PARABOLIC differential equations , *ALGORITHMS , *MATHEMATICAL models , *NUMERICAL analysis , *MATHEMATICAL mappings - Abstract
Abstract: This work studies an inverse problem of determining the first-order coefficient of degenerate parabolic equations using the measurement data specified at a fixed internal point. Being different from other ordinary parameter identification problems in parabolic equations, in our mathematical model there exists degeneracy on the lateral boundaries of the domain, which may cause the corresponding boundary conditions to go missing. By the contraction mapping principle, the uniqueness of the solution for the inverse problem is proved. A numerical algorithm on the basis of the predictor–corrector method is designed to obtain the numerical solution and some typical numerical experiments are also performed in the paper. The numerical results show that the proposed method is stable and the unknown function is recovered very well. The results obtained in the paper are interesting and useful, and can be extended to other more general inverse coefficient problems of degenerate PDEs. [Copyright &y& Elsevier]
- Published
- 2011
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- View/download PDF
11. Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains
- Author
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Aarão, J., Bradshaw-Hajek, B.H., Miklavcic, S.J., and Ward, D.A.
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NUMERICAL analysis , *EIGENFUNCTIONS , *BOUNDARY value problems , *ALGORITHMS , *BOUNDARY element methods , *MATHEMATICAL analysis - Abstract
Abstract: In a recent paper by the current authors a new methodology called the Extended-Domain-Eigenfunction-Method (EDEM) was proposed for solving elliptic boundary value problems on annular-like domains. In this paper we present and investigate one possible numerical algorithm to implement the EDEM. This algorithm is used to solve modified Helmholtz BVPs on annular-like domains. Two examples of annular-like domains are studied. The results and performance are compared with those of the well-known boundary element method (BEM). The high accuracy of the EDEM solutions and the superior efficiency of the EDEM over the BEM, make EDEM an excellent alternate candidate to use in the animation industry, where speed is a predominant requirement, and by the scientific community where accuracy is the paramount objective. [ABSTRACT FROM AUTHOR]
- Published
- 2011
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- View/download PDF
12. Multiscale algorithm with high accuracy for the elastic equations in three-dimensional honeycomb structures
- Author
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Liu, Xiao-Qi, Cao, Li-Qun, and Zhu, Qi-Ding
- Subjects
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HONEYCOMB structures , *ALGORITHMS , *DIMENSIONAL analysis , *NUMERICAL analysis , *FINITE element method , *ASYMPTOTIC homogenization - Abstract
Abstract: In this paper, we consider the elastomechanical problems of a honeycomb structure of composite materials. A multiscale finite element method and the postprocessing technique with high accuracy are presented. We will derive the proofs of all theoretical results. Finally, some numerical tests validate the theoretical results of this paper. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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13. Interpolation of Lipschitz functions
- Author
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Beliakov, Gleb
- Subjects
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NUMERICAL analysis , *INTERPOLATION , *ALGORITHMS , *CONTINUOUS functions - Abstract
Abstract: This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data. [Copyright &y& Elsevier]
- Published
- 2006
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14. CONDOR, a new parallel, constrained extension of Powell's UOBYQA algorithm: Experimental results and comparison with the DFO algorithm
- Author
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Vanden Berghen, Frank and Bersini, Hugues
- Subjects
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NUMERICAL analysis , *PARALLEL computers , *PARTIAL differential equations , *ALGORITHMS - Abstract
Abstract: This paper presents an algorithmic extension of Powell''s UOBYQA algorithm (Unconstrained Optimization BY Quadratical Approximation). We start by summarizing the original algorithm of Powell and by presenting it in a more comprehensible form. Thereafter, we report comparative numerical results between UOBYQA, DFO and a parallel, constrained extension of UOBYQA that will be called in the paper CONDOR (COnstrained, Non-linear, Direct, parallel Optimization using trust Region method for high-computing load function). The experimental results are very encouraging and validate the approach. They open wide possibilities in the field of noisy and high-computing-load objective functions optimization (from 2min to several days) like, for instance, industrial shape optimization based on computation fluid dynamic codes or partial differential equations solvers. Finally, we present a new, easily comprehensible and fully stand-alone implementation in C++ of the parallel algorithm. [Copyright &y& Elsevier]
- Published
- 2005
- Full Text
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15. Solving systems of IVPs with discontinuous derivatives—Numerical experiments.
- Author
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Goćwin, Maciej
- Subjects
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NUMERICAL analysis , *ALGORITHMS , *DERIVATIVES (Mathematics) , *HYPERSURFACES , *ERROR analysis in mathematics - Abstract
We deal in this paper with solving IVPs with singular right-hand side. We consider two recent algorithms of Kacewicz and Przybyłowicz for solving systems of IVPs with right-hand side functions which are globally Lipschitz continuous and piecewise r -smooth with piecewise Hölder r th partial derivatives with Hölder exponent ρ ∈ ( 0 , 1 ] . The singularity hypersurface is defined by the zeros of an unknown event function. We run several numerical experiments to verify the theoretical results of Kacewicz and Przybyłowicz. Our tests confirm that the bounds on the error O ( n − ( r + ρ ) ) can be achieved with O ( n ) function evaluations, where n is a number of discretization points. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
16. A flexible and adaptive simpler block GMRES with deflated restarting for linear systems with multiple right-hand sides.
- Author
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Zhong, Hong-xiu, Wu, Gang, and Chen, Guo-liang
- Subjects
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GENERALIZED minimal residual method , *ADAPTIVE control systems , *LINEAR systems , *NUMERICAL analysis , *ALGORITHMS - Abstract
Block GMRES is one of the most popular algorithms for solving large non-Hermitian linear systems with multiple right-hand sides. The simpler block GMRES algorithm is a variation of block GMRES, which avoids the factorization of a block upper Hessenberg matrix; and it is much simpler to program and requires less work than block GMRES. However, theoretical results given in this paper indicate that it is less stable due to the ill-conditioning of the basis used. In order to overcome this difficulty, we propose an adaptive simpler block GMRES algorithm for large linear systems with multiple right-hand sides. Theoretical analysis is made to show the reason why the new algorithm is superior to its original counterpart. Moreover, we consider how to restart and precondition the adaptive simpler block GMRES algorithm, and propose a flexible and adaptive simpler block GMRES algorithm with deflated restarting. Numerical experiments show the numerical behavior of our new algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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17. Numerical analysis of an adsorption dynamic model at the air–water interface.
- Author
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Copetti, M.I.M., Fernández, J.R., Muñiz, M.C., and Núñez, C.
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NUMERICAL analysis , *AIR-water interfaces , *DYNAMIC models , *STOCHASTIC convergence , *ALGORITHMS , *UNIQUENESS (Mathematics) , *LANGMUIR isotherms - Abstract
In this paper we deal with the numerical analysis of an adsorption dynamic model arising in a surfactant solution at the air–water interface; the diffusion model is considered together with the so-called Langmuir isotherm. An existence and uniqueness result is stated. Then, fully discrete approximations are introduced by using a finite element method and a hybrid combination of backward and forward Euler schemes. Error estimates are proved from which, under adequate additional regularity conditions, the linear convergence of the algorithm is derived assuming a dependence between both spatial and time discretization parameters. Finally, some numerical simulations are presented in order to demonstrate the accuracy of the algorithm and the behaviour of the solution for two commercially available surfactants. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
18. A trust-region SQP method without a penalty or a filter for nonlinear programming.
- Author
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Huang, Mingxia and Pu, Dingguo
- Subjects
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SEQUENTIAL analysis , *STOCHASTIC convergence , *ALGORITHMS , *NUMERICAL analysis , *NONLINEAR programming - Abstract
In this paper we present a new trust-region SQP algorithm for nonlinear programming. This method avoids using a penalty function, nor a filter, and instead establishes a new step acceptance mechanism. Under some reasonable assumptions, the method can be proved to be globally convergent to a KT point. Preliminary numerical experiments are presented that show the potential efficiency of the new approach. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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19. Explicit algorithms for multiwise merging of Bézier curves.
- Author
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Lu, Lizheng
- Subjects
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ALGORITHMS , *CURVES , *SCHEMES (Algebraic geometry) , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
This paper presents a novel scheme, called C r , s multiwise merging , for merging multiple segments of Bézier curves using a single Bézier curve. It is considered as an extension of the existing pairwise merging, to avoid the limitations caused by recursively applying pairwise merging to the multiple case. An explicit algorithm is developed to obtain the merged curve, which preserves C r and C s continuity at the endpoints and is optimal in the sense that the L 2 or l 2 distance is minimized. As an application we develop explicit algorithms for G 1 multiwise merging, always producing better results than C 1 multiwise merging. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
20. On the numerical solution of a Stefan problem with finite extinction time.
- Author
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Vynnycky, M. and Mitchell, S.L.
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NUMERICAL analysis , *PROBLEM solving , *SCHEMES (Algebraic geometry) , *FINITE differences , *ALGORITHMS - Abstract
In many phase-change problems of practical interest, it is important to know when a phase is depleted, a quantity referred to as the extinction time; however, there are no numerical schemes that are able to compute this with any degree of rigour or formal accuracy. In this paper, we develop such a scheme for the one-dimensional time-dependent problem of an evaporating spherical droplet. The Keller box finite-difference scheme is used, in tandem with the so-called boundary immobilization method. An important component of the work is the careful use of variable transformations that must be built into the numerical algorithm in order to preserve second-order accuracy in both time and space, in particular as regards resolving a square-root singularity in the droplet radius as the extinction time is approached. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
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21. ML(n)BiCGStabt: A ML(n)BiCGStab variant with A-transpose.
- Author
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Man-Chung Yeung
- Subjects
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KRYLOV subspace , *SUBSPACES (Mathematics) , *ALGORITHMS , *TOPOLOGICAL spaces , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
The 1980 IDR method (Wesseling and Sonneveld, 1980 [12]) plays an important role in the history of Krylov subspace methods. It started the research of transpose-free Krylov subspace methods. The ML(n)BiCGStab method (Yeung, 2012) is one of such methods. In this paper, we present a new ML(n)BiCGStab variant that involves A-transpose in its implementation. Comparison of this new algorithm with the existing ML(n)BiCGStab algorithms and some other Krylov subspace algorithms will be presented. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
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22. An improved generalized conjugate residual squared algorithm suitable for distributed parallel computing.
- Author
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Zuo, Xian-Yu, Zhang, Li-Tao, and Gu, Tong-Xiang
- Subjects
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DISTRIBUTED computing , *GENERALIZATION , *ALGORITHMS , *NUMERICAL analysis , *PARALLEL computers , *ITERATIVE methods (Mathematics) - Abstract
Abstract: In this paper, based on GCRS algorithm in Zhang and Zhao (2010) and the ideas in Gu et al. (2007), we present an improved generalized conjugate residual squared (IGCRS) algorithm that is designed for distributed parallel environments. The new improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS algorithm in such a way that all inner products per iteration are independent so that communication time required for inner products can be overlapped with useful computation. Theoretical analysis and numerical comparison of isoefficiency analysis show that the IGCRS method has better parallelism and scalability than the GCRS method, and the parallel performance can be improved by a factor of about 2. Finally, some numerical experiments clearly show that the IGCRS method can achieve better parallel performance with a higher scalability than the GCRS method and the improvement percentage of communication is up to 52.19% averagely, which meets our theoretical analysis. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
23. Algorithms for the Geronimus transformation for orthogonal polynomials on the unit circle.
- Author
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Humet, Matthias and Van Barel, Marc
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ALGORITHMS , *ORTHOGONAL polynomials , *BILINEAR transformation method , *FUNCTIONAL analysis , *NUMERICAL analysis , *JACOBI polynomials - Abstract
Abstract: Let be a positive definite bilinear functional on the unit circle defined on , the space of polynomials of degree at most . Then its Geronimus transformation is defined by for all , . Given , there are infinitely many such which can be described by a complex free parameter. The Hessenberg matrix that appears in the recurrence relations for orthogonal polynomials on the unit circle is unitary, and can be factorized using its associated Schur parameters. Recent results show that the unitary Hessenberg matrices associated with and , respectively, are related by a QR step where all the matrices involved are of order . For the analogue on the real line of this so-called spectral transformation, the tridiagonal Jacobi matrices associated with the respective functionals are related by an LR step. In this paper we derive algorithms that compute the new Schur parameters after applying a Geronimus transformation. We present two forward algorithms and one backward algorithm. The QR step between unitary Hessenberg matrices plays a central role in the derivation of each of the algorithms, where the main idea is to do the inverse of a QR step. Making use of the special structure of unitary Hessenberg matrices, all the algorithms are efficient and need only flops. We present several numerical experiments to analyse the accuracy and to explain the behaviour of the algorithms. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
24. Petviashvili type methods for traveling wave computations: I. Analysis of convergence.
- Author
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Álvarez, J. and Durán, A.
- Subjects
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TRAVELING waves (Physics) , *STOCHASTIC convergence , *FIXED point theory , *ALGORITHMS , *NUMERICAL analysis , *NONLINEAR equations - Abstract
Abstract: In this paper a family of fixed point algorithms for the numerical resolution of some systems of nonlinear equations is designed and analyzed. The family introduced here generalizes the Petviashvili method and can be applied to the numerical generation of traveling waves in some nonlinear dispersive systems. Conditions for the local convergence are derived and numerical comparisons between different elements of the family are carried out. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
25. A reweighted nuclear norm minimization algorithm for low rank matrix recovery.
- Author
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Li, Yu-Fan, Zhang, Yan-Jiao, and Huang, Zheng-Hai
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MATRIX norms , *ALGORITHMS , *FIXED point theory , *APPROXIMATION theory , *ITERATIVE methods (Mathematics) , *MATHEMATICAL sequences , *NUMERICAL analysis - Abstract
Abstract: In this paper, we propose a reweighted nuclear norm minimization algorithm based on the weighted fixed point method (RNNM–WFP algorithm) to recover a low rank matrix, which iteratively solves an unconstrained minimization problem introduced as a nonconvex smooth approximation of the low rank matrix minimization problem. We prove that any accumulation point of the sequence generated by the RNNM–WFP algorithm is a stationary point of the minimization problem. Numerical experiments on randomly generated matrix completion problems indicate that the proposed algorithm has better recoverability compared to existing iteratively reweighted algorithms. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
26. Adaptive ODE solvers in extended Kalman filtering algorithms.
- Author
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Kulikova, M.V. and Kulikov, G.Yu.
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ORDINARY differential equations , *KALMAN filtering , *ALGORITHMS , *NUMERICAL analysis , *HYBRID systems - Abstract
Abstract: This paper studies numerical methods that are used to treat ordinary differential equations arising in extended Kalman filtering algorithms. Such problems are called the moment equations and constitute an important subclass of differential equations. They all possess a number of specific properties that make the standard available software ineffective for some mathematical models in this area. For instance, we show that built-in Matlab ODE solvers are not able to cope with a number of tests considered here. In contrast, the hybrid method developed by Mazzoni (2007) exhibits much better performance on the same examples. The latter means that specially designed numerical schemes are needed for efficient solution of the moment equations instead of the standard software designed for general systems of ordinary differential equations. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
27. Numerical computation of bifurcations in large equilibrium systems in matlab.
- Author
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Bindel, D., Friedman, M., Govaerts, W., Hughes, J., and Kuznetsov, Yu.A.
- Subjects
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NUMERICAL analysis , *BIFURCATION theory , *EQUILIBRIUM , *INVARIANT subspaces , *ALGORITHMS , *SMOOTHNESS of functions , *PARAMETER estimation - Abstract
The Continuation of Invariant Subspaces (CIS) algorithm produces a smoothly-varying basis for an invariant subspace of a parameter-dependent matrix . We have incorporated the CIS algorithm into Cl_matcont, a Matlab package for the study of dynamical systems and their bifurcations. Using subspace reduction, we extend the functionality of Cl_matcont to large-scale computations of bifurcations of equilibria. In this paper, we describe the algorithms and functionality of the resulting Matlab bifurcation package Cl_matcontL. The novel features include: new CIS-based, continuous, well-scaled test functions for codimension 1 and 2 bifurcations; detailed description of locators for large problems; and examples of bifurcation analysis in large sparse problems. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
28. Parametric dominant pole algorithm for parametric model order reduction.
- Author
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Saadvandi, Maryam, Meerbergen, Karl, and Desmet, Wim
- Subjects
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PARAMETRIC modeling , *ALGORITHMS , *APPROXIMATION theory , *DYNAMICAL systems , *TIME delay systems , *NUMERICAL analysis - Abstract
Abstract: Standard model order reduction techniques attempt to build reduced order models of large scale systems with similar input–output behavior over a wide range of input frequencies as the full system models. The method known as the dominant pole algorithm has previously been successfully used in combination with model order reduction techniques to approximate standard linear time-invariant dynamical systems and second order dynamical systems as well as nonlinear time-delay systems. In this paper, we show that the dominant pole algorithm can be adapted for parametric systems where these parameters usually have physical meaning. There are two approaches for finding dominant poles. These algorithms are illustrated by the second order numerical examples. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
29. A convex optimization method to solve a filter design problem.
- Author
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Le, Thanh Hieu and Van Barel, Marc
- Subjects
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CONVEX domains , *MATHEMATICAL optimization , *MATHEMATICAL formulas , *PARAMETER estimation , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: In this paper, we formulate the feasibility problem corresponding to a filter design problem as a convex optimization problem. Combined with a bisection rule, this leads to an algorithm for minimizing the design parameter in the filter design problem. A safety margin is introduced to solve the numerical difficulties when solving this type of problem numerically. Numerical experiments illustrate the validity of this approach for larger degrees of the filter as compared to similar previous algorithms. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
30. DGFEM for dynamical systems describing interaction of compressible fluid and structures.
- Author
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Feistauer, Miloslav, Hasnedlová-Prokopová, Jaroslava, Horáček, Jaromír, Kosík, Adam, and Kučera, Václav
- Subjects
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GALERKIN methods , *NUMERICAL analysis , *VIBRATION (Mechanics) , *ELASTICITY , *DEPENDENCE (Statistics) , *MATHEMATICAL formulas , *ALGORITHMS - Abstract
Abstract: The paper is concerned with the numerical solution of flow-induced vibrations of elastic structures. The dependence on time of the domain occupied by the fluid is taken into account with the aid of the ALE (Arbitrary Lagrangian–Eulerian) formulation of the compressible Navier–Stokes equations. The deformation of the elastic body, caused by aeroelastic forces, is described by the linear dynamical elasticity equations. These two systems are coupled by transmission conditions. The flow problem is discretized by the discontinuous Galerkin finite element method (DGFEM) in space and by the backward difference formula (BDF) in time. The structural problem is discretized by conforming finite elements and the Newmark method. The fluid–structure interaction is realized via weak or strong coupling algorithms. The developed technique is tested by numerical experiments and applied to the simulation of vibrations of vocal folds during phonation onset. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
31. Accurate evaluation of the -th derivative of a polynomial and its application
- Author
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Jiang, Hao, Graillat, Stef, Hu, Canbin, Li, Shengguo, Liao, Xiangke, Cheng, Lizhi, and Su, Fang
- Subjects
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POLYNOMIALS , *ALGORITHMS , *FORWARD error correction , *ERROR analysis in mathematics , *ACCURACY , *NUMERICAL analysis - Abstract
Abstract: This paper presents a compensated algorithm for the evaluation of the -th derivative of a polynomial in power basis. The proposed algorithm makes it possible the direct evaluation without obtaining the -th derivative expression of the polynomial itself, with a very accurate result to all but the most ill-conditioned evaluation. Forward error analysis and running error analysis are performed by an approach based on the data dependency graph. Numerical experiments illustrate the accuracy and efficiency of the algorithm. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
32. A symbolic-numerical approach to approximate parameterizations of space curves using graphs of critical points
- Author
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Bizzarri, Michal and Lávička, Miroslav
- Subjects
- *
CRITICAL point theory , *NUMERICAL analysis , *APPROXIMATION theory , *PARAMETERIZATION , *GRAPH theory , *ALGORITHMS - Abstract
Abstract: A simple algorithm for computing an approximate parameterization of real space algebraic curves using their graphs of critical points is designed and studied in this paper. The first step is determining a suitable space graph which contains all critical points of a real algebraic space curve implicitly defined as the complete intersection of two surfaces. The construction of this graph is based on one projection of in a general position onto an -plane and on an intentional choice of vertices. The second part of the designed method is a computation of a spline curve which replaces the edges of the constructed graph by segments of a chosen free-form curve. This step is formulated as an optimization problem when the objective function approximates the integral of the squared Euclidean distance of the constructed approximate curve to the intersection curve. The presented method, based on combining symbolic and numerical steps to the approximation problem, provides approximate parameterizations of space algebraic curves from a small number of approximating arcs. It may serve as a first step to several problems originating in technical practice where approximation curve parameterizations are needed. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
33. A new structure-preserving method for quaternion Hermitian eigenvalue problems
- Author
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Jia, Zhigang, Wei, Musheng, and Ling, Sitao
- Subjects
- *
QUATERNIONS , *HERMITIAN structures , *EIGENVALUES , *MATRICES (Mathematics) , *ALGORITHMS , *ORTHOGONALIZATION , *MATHEMATICAL transformations , *NUMERICAL analysis - Abstract
Abstract: In this paper we propose a novel structure-preserving algorithm for solving the right eigenvalue problem of quaternion Hermitian matrices. The algorithm is based on the structure-preserving tridiagonalization of the real counterpart for quaternion Hermitian matrices by applying orthogonal -symplectic matrices. The algorithm is numerically stable because we use orthogonal transformations; the algorithm is very efficient, it costs about a quarter arithmetical operations, and a quarter to one-eighth CPU times, comparing with standard general-purpose algorithms. Numerical experiments are provided to demonstrate the efficiency of the structure-preserving algorithm. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
34. Computation of matrix functions with deflated restarting
- Author
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Gu, Chuanqing and Zheng, Lin
- Subjects
- *
MATRIX functions , *KRYLOV subspace , *APPROXIMATION theory , *ALGORITHMS , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
Abstract: A deflated restarting Krylov subspace method for approximating a function of a matrix times a vector is proposed. In contrast to other Krylov subspace methods, the performance of the method in this paper is better. We further show that the deflating algorithm inherits the superlinear convergence property of its unrestarted counterpart for the entire function and present the results of numerical experiments. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
35. Option pricing with a direct adaptive sparse grid approach
- Author
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Bungartz, Hans-Joachim, Heinecke, Alexander, Pflüger, Dirk, and Schraufstetter, Stefanie
- Subjects
- *
OPTIONS (Finance) , *PRICING , *SPARSE matrices , *ALGORITHMS , *FINITE element method , *GRID computing , *NUMERICAL analysis - Abstract
Abstract: We present an adaptive sparse grid algorithm for the solution of the Black–Scholes equation for option pricing, using the finite element method. Sparse grids enable us to deal with higher-dimensional problems better than full grids. In contrast to common approaches that are based on the combination technique, which combines different solutions on anisotropic coarse full grids, the direct sparse grid approach allows for local adaptive refinement. When dealing with non-smooth payoff functions, this reduces the computational effort significantly. In this paper, we introduce the spatially adaptive discretization of the Black–Scholes equation with sparse grids and describe the algorithmic structure of the numerical solver. We present several strategies for adaptive refinement, evaluate them for different dimensionalities, and demonstrate their performance showing numerical results. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
36. Two-stage least squares and indirect least squares algorithms for simultaneous equations models
- Author
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López-Espín, Jose J., Vidal, Antonio M., and Giménez, Domingo
- Subjects
- *
LEAST squares , *ALGORITHMS , *MATHEMATICAL decomposition , *MULTICORE processors , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: This paper analyzes the solution of simultaneous equations models. Efficient algorithms for the two-stage least squares method using QR-decomposition are developed and studied. The reduction of the execution time when the structure of the matrices in each equation is exploited is analyzed theoretically and experimentally. An efficient algorithm for the indirect least squares method is developed. Some techniques are used to accelerate the solution of the problem: parallel versions for multicore systems, and extensive use of the MKL library, thus obtaining efficient, portable versions of the algorithms. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
37. Finding all solutions of separable systems of piecewise-linear equations using integer programming
- Author
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Yamamura, Kiyotaka and Tamura, Naoya
- Subjects
- *
SEPARABLE algebras , *LINEAR differential equations , *INTEGER programming , *NONLINEAR differential equations , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: Finding all solutions of nonlinear or piecewise-linear equations is an important problem which is widely encountered in science and engineering. Various algorithms have been proposed for this problem. However, the implementation of these algorithms are generally difficult for non-experts or beginners. In this paper, an efficient method is proposed for finding all solutions of separable systems of piecewise-linear equations using integer programming. In this method, we formulate the problem of finding all solutions by a mixed integer programming problem, and solve it by a high-performance integer programming software such as GLPK, SCIP, or CPLEX. It is shown that the proposed method can be easily implemented without making complicated programs. It is also confirmed by numerical examples that the proposed method can find all solutions of medium-scale systems of piecewise-linear equations in practical computation time. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
38. Binary weighted essentially non-oscillatory (BWENO) approximation
- Author
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Crnković, Bojan and Črnjarić-Žic, Nelida
- Subjects
- *
BINARY number system , *OSCILLATION theory of differential equations , *APPROXIMATION theory , *INTERPOLATION , *SMOOTHNESS of functions , *NUMERICAL analysis , *HYPERBOLIC differential equations , *ALGORITHMS - Abstract
Abstract: Weighted essentially non-oscillatory (WENO) schemes have been mainly used for solving hyperbolic partial differential equations (PDEs). Such schemes are capable of high order approximation in smooth regions and non-oscillatory sharp resolution of discontinuities. The base of the WENO schemes is a non-oscillatory WENO approximation procedure, which is not necessarily related to PDEs. The typical WENO procedures are WENO interpolation and WENO reconstruction. The WENO algorithm has gained much popularity but the basic idea of approximation did not change much over the years. In this paper, we first briefly review the idea of WENO interpolation and propose a modification of the basic algorithm. New approximation should improve basic characteristics of the approximation and provide a more flexible framework for future applications. New WENO procedure involves a binary tree weighted construction that is based on key ideas of WENO algorithm and we refer to it as the binary weighted essentially non-oscillatory (BWENO) approximation. New algorithm comes in a rational and a polynomial version. Furthermore, we describe the WENO reconstruction procedure, which is usually involved in the numerical schemes for hyperbolic PDEs, and propose the new reconstruction procedure based on the described BWENO interpolation. The obtained numerical results show that the newly proposed procedures perform very well on the considered test examples. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
39. Geometry of total variation regularized -model
- Author
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Shi, Yuying, Wang, Li-Lian, and Tai, Xue-Cheng
- Subjects
- *
GEOMETRY , *ALGORITHMS , *MATHEMATICAL regularization , *MATHEMATICAL models , *LAGRANGIAN functions , *NUMERICAL analysis - Abstract
Abstract: In this paper, the geometry and scale selection properties of the total variation (TV) regularized -model are rigorously analyzed. Some intrinsic features different from the TV- model are derived and demonstrated. Numerical algorithms based on recent developed augmented Lagrangian methods are implemented and numerical results consistent with the theoretical results are provided. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
40. Detection of point-like scatterers using one type of scattered elastic waves
- Author
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Gintides, Drossos, Sini, Mourad, and Thành, Nguyen Trung
- Subjects
- *
ELASTIC wave scattering , *AFFIRMATIONS (Self-help) , *LOCALIZATION theory , *ALGORITHMS , *NUMERICAL analysis , *APPLIED mathematics - Abstract
Abstract: In this paper, we are concerned with the detection of point-like obstacles using elastic waves. We show that one type of waves, either the or the scattered waves, is enough for localizing the points. We also show how the use of incident waves gives better resolution than the waves. These affirmations are demonstrated by several numerical examples using a MUSIC type algorithm. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
41. A mountain pass algorithm with projector
- Author
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Tacheny, N. and Troestler, C.
- Subjects
- *
ALGORITHMS , *MOUNTAIN passes , *MAXIMA & minima , *FIXED point theory , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
Abstract: In this paper, we present an enhanced version of the minimax algorithm of Chen, Ni, and Zhou that offers the additional guarantee that the solution found is a fix-point of a projector on a cone. Positivity, negativity, and monotonicity can be expressed in this way. The convergence of the algorithm is proved by means of a “computational deformation lemma” instead of the usual deformation lemma used in the calculus of variations. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
42. Dual approaches to finite element model updating
- Author
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Yuan, Quan
- Subjects
- *
FINITE element method , *MATHEMATICAL models , *MATRICES (Mathematics) , *APPROXIMATION theory , *MAXIMA & minima , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: The problem of finding the least change adjustment to a stiffness matrix modeled by finite element method is considered in this paper. Desired stiffness matrix properties such as symmetry, sparsity, positive semidefiniteness, and satisfaction of the characteristic equation are imposed as side constraints of the constructed optimal matrix approximation for updating the stiffness matrix, which matches measured data better. The dual problems of the original constrained minimization are presented and solved by subgradient algorithms with different line search strategies. Some numerical results are included to illustrate the performance and application of the proposed methods. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
43. A numerical algorithm for nonlinear multi-point boundary value problems
- Author
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Geng, F.Z.
- Subjects
- *
NUMERICAL analysis , *ALGORITHMS , *NONLINEAR systems , *BOUNDARY value problems , *PROBLEM solving , *ITERATIVE methods (Mathematics) , *KERNEL functions - Abstract
Abstract: In this paper, an algorithm is presented for solving second-order nonlinear multi-point boundary value problems (BVPs). The method is based on an iterative technique and the reproducing kernel method (RKM). Two numerical examples are provided to show the reliability and efficiency of the present method. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
44. Block Arnoldi-based methods for large scale discrete-time algebraic Riccati equations
- Author
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Bouhamidi, A., Heyouni, M., and Jbilou, K.
- Subjects
- *
DISCRETE-time systems , *RICCATI equation , *APPROXIMATION theory , *GRAPHICAL projection , *NEWTON-Raphson method , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: In the present paper, we present block Arnoldi-based methods for the computation of low rank approximate solutions of large discrete-time algebraic Riccati equations (DARE). The proposed methods are projection methods onto block or extended block Krylov subspaces. We give new upper bounds for the norm of the error obtained by applying these block Arnoldi-based processes. We also introduce the Newton method combined with the block Arnoldi algorithm and present some numerical experiments with comparisons between these methods. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
45. A novel method for computation of higher order singular points in nonlinear problems with single parameter
- Author
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Wei, Jun-qiang and Yang, Zhong-hua
- Subjects
- *
MATHEMATICAL singularities , *NONLINEAR differential equations , *CONTINUATION methods , *HOMOTOPY theory , *NUMERICAL analysis , *ALGORITHMS - Abstract
Abstract: This paper deals with unusual numerical techniques for computation of higher order singular points in nonlinear problems with single parameter. Based on the uniformly extended system, a unified algorithm combining the homotopy and the pseudo-arclength continuation method is given. Properties of the uniformly augmented system are listed and proved. The effectiveness of the proposed algorithm is testified by three numerical examples. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
46. A working set SQCQP algorithm with simple nonmonotone penalty parameters
- Author
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Tang, Chun-Ming, Jian, Jin-Bao, and Li, Guo-Yin
- Subjects
- *
QUADRATIC programming , *SEQUENTIAL analysis , *ALGORITHMS , *MONOTONE operators , *MULTIPLIERS (Mathematical analysis) , *NUMERICAL analysis , *STOCHASTIC convergence , *CONVEX domains - Abstract
Abstract: In this paper, we present a new sequential quadratically constrained quadratic programming (SQCQP) algorithm, in which a simple updating strategy of the penalty parameter is adopted. This strategy generates nonmonotone penalty parameters at early iterations and only uses the multiplier corresponding to the bound constraint of the quadratically constrained quadratic programming (QCQP) subproblem instead of the multipliers of the quadratic constraints, which will bring some numerical advantages. Furthermore, by using the working set technique, we remove the constraints of the QCQP subproblem that are locally irrelevant, and thus the computational cost could be reduced. Without assuming the convexity of the objective function or the constraints, the algorithm is proved to be globally, superlinearly and quadratically convergent. Preliminary numerical results show that the proposed algorithm is very promising when compared with the tested SQP algorithms. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
47. On finite difference approximation of a matrix-vector product in the Jacobian-free Newton–Krylov method
- Author
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An, Heng-Bin, Wen, Ju, and Feng, Tao
- Subjects
- *
FINITE differences , *APPROXIMATION theory , *VECTOR analysis , *NEWTON-Raphson method , *JACOBIAN matrices , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: The Jacobian-free Newton–Krylov (JFNK) method is a special kind of Newton–Krylov algorithm, in which the matrix-vector product is approximated by a finite difference scheme. Consequently, it is not necessary to form and store the Jacobian matrix. This can greatly improve the efficiency and enlarge the application area of the Newton–Krylov method. The finite difference scheme has a strong influence on the accuracy and robustness of the JFNK method. In this paper, several methods for approximating the Jacobian-vector product, including the finite difference scheme and the finite difference step size, are analyzed and compared. Numerical results are given to verify the effectiveness of different finite difference methods. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
48. Numerical algorithms and simulations for reflected backward stochastic differential equations with two continuous barriers
- Author
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Xu, Mingyu
- Subjects
- *
NUMERICAL analysis , *ALGORITHMS , *SIMULATION methods & models , *STOCHASTIC differential equations , *CONTINUOUS functions , *WIENER processes , *TREE graphs - Abstract
Abstract: In this paper we study different algorithms for reflected backward stochastic differential equations (BSDE in short) with two continuous barriers based on the framework of using a binomial tree to simulate 1-d Brownian motion. We introduce numerical algorithms by the penalization method and the reflected method, respectively. In the end simulation results are also presented. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
49. A metamodel-assisted evolutionary algorithm for expensive optimization
- Author
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Luo, Changtong, Zhang, Shao-Liang, Wang, Chun, and Jiang, Zonglin
- Subjects
- *
MATHEMATICAL models , *EVOLUTIONARY computation , *ALGORITHMS , *MATHEMATICAL optimization , *GLOBAL analysis (Mathematics) , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
Abstract: Expensive optimization aims to find the global minimum of a given function within a very limited number of function evaluations. It has drawn much attention in recent years. The present expensive optimization algorithms focus their attention on metamodeling techniques, and call existing global optimization algorithms as subroutines. So it is difficult for them to keep a good balance between model approximation and global search due to their two-part property. To overcome this difficulty, we try to embed a metamodel mechanism into an efficient evolutionary algorithm, low dimensional simplex evolution (LDSE), in this paper. The proposed algorithm is referred to as the low dimensional simplex evolution extension (LDSEE). It is inherently parallel and self-contained. This renders it very easy to use. Numerical results show that our proposed algorithm is a competitive alternative for expensive optimization problems. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
50. Convergence of a FEM and two-grid algorithms for elliptic problems on disjoint domains
- Author
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Jovanovic, Boško S., Koleva, Miglena N., and Vulkov, Lubin G.
- Subjects
- *
STOCHASTIC convergence , *FINITE element method , *ALGORITHMS , *MATHEMATICAL decoupling , *NUMERICAL analysis , *RECTANGLES , *PROBLEM solving - Abstract
Abstract: In this paper, we analyze a FEM and two-grid FEM decoupling algorithms for elliptic problems on disjoint domains. First, we study the rate of convergence of the FEM and, in particular, we obtain a superconvergence result. Then with proposed algorithms, the solution of the multi-component domain problem (simple example — two disjoint rectangles) on a fine grid is reduced to the solution of the original problem on a much coarser grid together with solution of several problems (each on a single-component domain) on fine meshes. The advantage is the computational cost although the resulting solution still achieves asymptotically optimal accuracy. Numerical experiments demonstrate the efficiency of the algorithms. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
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