18 results
Search Results
2. A Concave FE-BI-MLFMA for Scattering by a Large Body With Nonuniform Deep Cavities.
- Author
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Yang, Ming-Lin, Sheng, Xin-Qing, Pan, Xiao-Min, and Pi, Wei-Chao
- Subjects
- *
CONCAVE functions , *FINITE element method , *ALGORITHMS , *CAVITY resonators , *SPARSE matrices , *STOCHASTIC convergence , *APPROXIMATION theory , *NUMERICAL analysis - Abstract
A concave finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) is presented for scattering by a large body with nonuniform deep cavities. Different from the conventional FE-BI-MLFMA, the boundary integral equation in this concave FE-BI-MLFMA is established on a concave surface to reduce the region of the finite element method (FEM), which can significantly reduce the dispersion error from the FEM and improve the efficiency of FE-BI-MLFMA especially for nonuniform cavities. To eliminate the problem of slow convergence caused by concave surface, an efficient preconditioner based on the sparse approximate inverse (SAI) is constructed in this paper. Numerical performance of the constructed preconditioner based on the SAI is investigated in detail. Numerical experiments demonstrate the accuracy and efficiency of this SAI preconditioned concave FE-BI-MLFMA for nonuniform deep and large cavites. This SAI preconditioned concave FE-BI-MLFMA is parallelized to further improve its capability in this paper. An extremely big and deep nonuniform cavity has been calculated, demonstrating the great capability of this parallel concave FE-BI-MLFMA. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
- Full Text
- View/download PDF
3. On the Method of Shortest Residuals for Unconstrained Optimization.
- Author
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Pytlak, R. and Tarnawski, T.
- Subjects
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CONJUGATE gradient methods , *APPROXIMATION theory , *NUMERICAL solutions to equations , *ITERATIVE methods (Mathematics) , *MATHEMATICAL optimization , *ALGORITHMS , *STOCHASTIC convergence , *NUMERICAL analysis , *CALCULUS of variations - Abstract
The paper discusses several versions of the method of shortest residuals, a specific variant of the conjugate gradient algorithm, first introduced by Lemaréchal and Wolfe and discussed by Hestenes in a quadratic case. In the paper we analyze the global convergence of the versions considered. Numerical comparison of these versions of the method of shortest residuals and an implementation of a standard Polak–Ribière conjugate gradient algorithm is also provided. It supports the claim that the method of shortest residuals is a viable technique, competitive to other conjugate gradient algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
4. SM-Algorithms for Approximating the Variable-Order Fractional Derivative of High Order.
- Author
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Moghaddam, B. P. and Machado, J. A. T.
- Subjects
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FRACTIONAL calculus , *APPROXIMATION theory , *STOCHASTIC convergence , *NUMERICAL analysis , *ALGORITHMS - Abstract
In this paper we discuss different definitions of variable-order derivatives of high order and we propose accurate and robust algorithms for their approximate calculation. The proposed algorithms are based on finite difference approximations and B-spline interpolation. We compare the performance of the algorithms by experimental convergence order. Numerical examples are presented demonstrating the efficiency and accuracy of the proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
5. Coordinate descent algorithms.
- Author
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Wright, Stephen
- Subjects
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ALGORITHMS , *MATHEMATICAL optimization , *PROBLEM solving , *APPROXIMATION theory , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity continues to grow because of their usefulness in data analysis, machine learning, and other areas of current interest. This paper describes the fundamentals of the coordinate descent approach, together with variants and extensions and their convergence properties, mostly with reference to convex objectives. We pay particular attention to a certain problem structure that arises frequently in machine learning applications, showing that efficient implementations of accelerated coordinate descent algorithms are possible for problems of this type. We also present some parallel variants and discuss their convergence properties under several models of parallel execution. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
6. Generalized Laguerre spectral method for Fisher's equation on a semi-infinite interval.
- Author
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Wang, Tian-jun
- Subjects
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LAGUERRE geometry , *BOUNDARY value problems , *ALGORITHMS , *NUMERICAL analysis , *APPROXIMATION theory , *STOCHASTIC convergence - Abstract
In this paper, we propose a generalized Laguerre spectral method for Fisher's-type equation with inhomogeneous boundary conditions on a semi-infinite interval. By reformulating the equation with suitable functional transform, it is shown that the generalized Laguerre approximations are convergent on a semi-infinite interval with spectral accuracy. An efficient and accurate algorithm based on the generalized Laguerre approximations to the transformed equation is developed and implemented. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
- Full Text
- View/download PDF
7. A supplement to a regularization method for the proximal point algorithm.
- Author
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Saejung, Satit
- Subjects
ITERATIVE methods (Mathematics) ,STOCHASTIC convergence ,APPROXIMATION theory ,ALGORITHMS ,NUMERICAL analysis - Abstract
The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115-125, ) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226-240, ) and to give a supplement to these results. With the new technique proposed by Maingé (Comput Math Appl 59(1):74-79, ), we show that the convergence of the iterative scheme is established under another assumption. It is noted that if the computation error is zero or the approximate computation is exact, our new result is a genuine generalization of Xu's result and Kamimura-Takahashi's result. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
8. Computation of matrix functions with deflated restarting
- Author
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Gu, Chuanqing and Zheng, Lin
- Subjects
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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
9. Extrapolation algorithm of compact ADI approximation for two-dimensional parabolic equation
- Author
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Zhou, Han, Wu, Yu-Jiang, and Tian, WenYi
- Subjects
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EXTRAPOLATION , *ALGORITHMS , *COMPACTIFICATION (Mathematics) , *APPROXIMATION theory , *PARABOLIC differential equations , *STOCHASTIC convergence , *NUMERICAL analysis - Abstract
Abstract: In this paper, we propose a compact alternating direction implicit (ADI) scheme for solving the two-dimensional parabolic equation. The maximum norm convergence is proven, and the convergence rate is second-order in time and fourth-order in space. We develop a Richardson extrapolation algorithm to increase the accuracy to sixth-order both in time and space. Numerical experiments show the effectiveness of the method. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
10. A hybrid algorithm for approximate optimal control of nonlinear Fredholm integral equations.
- Author
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Borzabadi, AkbarH., Fard, OmidS., and Mehne, HamedH.
- Subjects
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ALGORITHMS , *FREDHOLM equations , *NONLINEAR theories , *ITERATIVE methods (Mathematics) , *STOCHASTIC convergence , *NUMERICAL analysis , *APPROXIMATION theory - Abstract
In this paper, a novel hybrid method based on two approaches, evolutionary algorithms and an iterative scheme, for obtaining the approximate solution of optimal control governed by nonlinear Fredholm integral equations is presented. By converting the problem to a discretized form, it is considered as a quasi-assignment problem and then an iterative method is applied to find an approximate solution for the discretized form of the integral equation. An analysis for convergence of the proposed iterative method and its implementation for numerical examples are also given. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
11. A new numerical approximation for Volterra integral equations combining two quadrature rules
- Author
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Mennouni, Abdelaziz
- Subjects
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VOLTERRA equations , *APPROXIMATION theory , *NUMERICAL analysis , *INTEGRAL equations , *ALGORITHMS , *STOCHASTIC convergence - Abstract
Abstract: This paper describes a numerical approximation to the solution of Volterra integral equations of the second kind. This algorithm combines trapezoidal and Simpson rules. We prove the convergence of the method. Numerical examples are provided to illustrate the accuracy of the method. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
12. A symmetric rank-one quasi-Newton line-search method using negative curvature directions.
- Author
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Öztoprak, Figen and Birbil, Ş.İlker
- Subjects
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MATHEMATICAL symmetry , *ITERATIVE methods (Mathematics) , *MATHEMATICAL optimization , *APPROXIMATION theory , *NUMERICAL analysis , *STOCHASTIC convergence , *ALGORITHMS - Abstract
We propose a quasi-Newton line-search method that uses negative curvature directions for solving unconstrained optimization problems. In this method, the symmetric rank-one (SR1) rule is used to update the Hessian approximation. The SR1 update rule is known to have a good numerical performance; however, it does not guarantee positive definiteness of the updated matrix. We first discuss the details of the proposed algorithm and then concentrate on its practical behaviour. Our extensive computational study shows the potential of the proposed method from different angles, such as its performance compared with some other existing packages, the profile of its computations, and its large-scale adaptation. We then conclude the paper with the convergence analysis of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
13. A new class of massively parallel direction splitting for the incompressible Navier–Stokes equations
- Author
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Guermond, J.L. and Minev, P.D.
- Subjects
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NAVIER-Stokes equations , *SET theory , *ALGORITHMS , *APPROXIMATION theory , *NUMERICAL analysis , *PERFORMANCE evaluation , *OPERATOR theory , *STOCHASTIC convergence - Abstract
Abstract: We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier–Stokes equations. The main originality of the method consists of using the operator (I − ∂ xx )(I − ∂ yy )(I − ∂ zz ) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2×109 points. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
14. Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology.
- Author
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Jouvet, Guillaume and Rappaz, Jacques
- Subjects
- *
FINITE element method , *STOKES equations , *NUMERICAL analysis , *STOCHASTIC convergence , *ALGORITHMS , *APPROXIMATION theory ,GLACIER speed - Abstract
The aim of this paper is to study a nonlinear stationary Stokes problem with mixed boundary conditions that describes the ice velocity and pressure fields of grounded glaciers under Glen's flow law. Using convex analysis arguments, we prove the existence and the uniqueness of a weak solution. A finite element method is applied with approximation spaces that satisfy the inf-sup condition, and a priori error estimates are established by using a quasinorm technique. Several algorithms including Newton's method are proposed to solve the nonlinearity of the Stokes problem and are proved to be convergent. Our results are supported by numerical convergence studies. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
15. A conic trust-region method and its convergence properties
- Author
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Qu, Shao-Jian, Jiang, Su-Da, and Zhu, Ying
- Subjects
- *
MATHEMATICAL optimization , *STOCHASTIC convergence , *APPROXIMATION theory , *ALGORITHMS , *NUMERICAL analysis - Abstract
Abstract: In this paper we consider a conic trust-region method for unconstrained optimization problems and analyze its convergence properties. We propose a convenient curvilinear search method to approximately solve the arising conic trust-region subproblem. Note that this approximate method preserves the strong convergence properties of the exact solution methods and is easy to implement. Both the linear and superlinear convergence of the method are established under commonly used conditions. Numerical experiments are conducted to show the efficiency of the new method. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
16. A De-Interlacing Algorithm Using Markov Random Field Model.
- Author
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Min Li and Truong Nguyen
- Subjects
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MARKOV random fields , *STOCHASTIC processes , *MATHEMATICAL optimization , *NUMERICAL analysis , *STOCHASTIC convergence , *APPROXIMATION theory , *INTERPOLATION , *ALGORITHMS - Abstract
In this paper, a motion-compensated de-interlacing algorithm using the Markov random field (MRF) model is proposed. The de-interlacing problem is formulated as a maximum a posteriori (MAP) MRF problem. The MAP solution is the one that minimizes an energy function, which imposes discontinuity-adaptive smoothness (DAS) spatial constraint on the de-interlaced frame. The edge direction information, which is used to formulate the DAS constraint, is implicitly indicated by weight vectors (weights for 16 digitized directions). Generally, large weights are assigned to along-edge directions and relatively small weights are assigned to across-edge directions. As a local statistical-based method, the proposed weighting method should be more robust than traditional edge-directed interpolation methods in deciding local edge directions. The proposed algorithm is implemented by an iterative optimization process, which guarantees convergence. However, a global optimal solution is not guaranteed due to computational complexity concern. Simulation results compare the proposed algorithm to other motion compensated de-interlacing algorithms. Significant improvements of de-interlaced edges are observed. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
17. Modification of theWolfe Line Search Rules to Satisfy the Descent Condition in the Polak-Ribière-Polyak Conjugate Gradient Method.
- Author
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Armand, P.
- Subjects
- *
CONJUGATE gradient methods , *APPROXIMATION theory , *CONSTRAINED optimization , *MATHEMATICAL optimization , *LINEAR differential equations , *LINEAR systems , *NUMERICAL analysis , *STOCHASTIC convergence , *ALGORITHMS - Abstract
This paper proposes a line search technique to satisfy a relaxed form of the strong Wolfe conditions in order to guarantee the descent condition at each iteration of the Polak-Ribière-Polyak conjugate gradient algorithm. It is proved that this line search algorithm preserves the usual convergence properties of any descent algorithm. In particular, it is shown that the Zoutendijk condition holds under mild assumptions. It is also proved that the resulting conjugate gradient algorithm is convergent under a strong convexity assumption. For the nonconvex case, a globally convergent modification is proposed. Numerical tests are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2007
- Full Text
- View/download PDF
18. Joint Design of Interpolation Filters and Decision Feedback Equalizers.
- Author
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Mu-Huo Cheng and Tsai-Sheng Kao
- Subjects
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ALGORITHMS , *ITERATIVE methods (Mathematics) , *NUMERICAL analysis , *INTERPOLATION , *APPROXIMATION theory , *STOCHASTIC convergence - Abstract
This paper presents an algorithm to design jointly interpolation filters and decision feedback equalizers in the sense of minimum mean-square error such that the joint capacity which is neglected in conventional design is explored to improve the receiver performance. The algorithm comprises an iteration of two alternating simple quadratic minimizing operations and ensures convergence. A simulation example for the raised-cosine channel demonstrates that via this approach an improvement over the conventional design can be achieved. [ABSTRACT FROM AUTHOR]
- Published
- 2005
- Full Text
- View/download PDF
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