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2. An elementary algorithm for computing the determinant of pentadiagonal Toeplitz matrices
- Author
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Cinkir, Zubeyir
- Subjects
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TOEPLITZ matrices , *DETERMINANTS (Mathematics) , *ALGORITHMS , *RATIONAL numbers , *MATHEMATICAL analysis - Abstract
Abstract: Over the last years, various fast algorithms for computing the determinant of a pentadiagonal Toeplitz matrices were developed. In this paper, we give a new kind of elementary algorithm requiring operations, where is an integer that needs to be chosen freely at the beginning of the algorithm. For example, we can compute in and operations if we choose as and , respectively. For various applications, it will be enough to test if the determinant of a pentadiagonal Toeplitz matrix is zero or not. As in another result of this paper, we used modular arithmetic to give a fast algorithm determining when determinants of such matrices are non-zero. This second algorithm works only for Toeplitz matrices with rational entries. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
3. Triangular Bézier sub-surfaces on a triangular Bézier surface
- Author
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Chen, Wenyu, Yu, Rongdong, Zheng, Jianmin, Cai, Yiyu, and Au, Chikit
- Subjects
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TRIANGULARIZATION (Mathematics) , *GEOMETRIC surfaces , *RECURSION theory , *OPERATOR theory , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bézier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
4. 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.
- Subjects
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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
- Full Text
- View/download PDF
5. Newton basis for multivariate Birkhoff interpolation
- Author
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Wang, Xiaoying, Zhang, Shugong, and Dong, Tian
- Subjects
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INTERPOLATION , *POLYNOMIALS , *NEWTON-Raphson method , *HERMITE polynomials , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: Multivariate Birkhoff interpolation is the most complex polynomial interpolation problem and people know little about it so far. In this paper, we introduce a special new type of multivariate Birkhoff interpolation and present a Newton paradigm for it. Using the algorithms proposed in this paper, we can construct a Hermite system for any interpolation problem of this type and then obtain a Newton basis for the problem w.r.t. the Hermite system. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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6. The multigrid algorithm applied to a degenerate equation: A convergence analysis
- Author
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Almendral Vázquez, Ariel and Fredrik Nielsen, Bjørn
- Subjects
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STOCHASTIC convergence , *PARTIAL differential equations , *ALGORITHMS , *MATHEMATICAL analysis ,MATHEMATICAL models of option - Abstract
Abstract: In this paper we analyze the convergence properties of the Multigrid Method applied to the Black–Scholes differential equation arising in mathematical finance. We prove, for the discretized single-asset Black–Scholes equation, that the multigrid -cycle possesses optimal convergence properties. Furthermore, through a series of numerical experiments we test the performance of the method for single-asset option problems. Throughout the paper we focus on models of European options. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
7. Weighted least squares solutions to general coupled Sylvester matrix equations
- Author
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Zhou, Bin, Li, Zhao-Yan, Duan, Guang-Ren, and Wang, Yong
- Subjects
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LEAST squares , *MATRICES (Mathematics) , *ITERATIVE methods (Mathematics) , *ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL analysis - Abstract
Abstract: This paper is concerned with weighted least squares solutions to general coupled Sylvester matrix equations. Gradient based iterative algorithms are proposed to solve this problem. This type of iterative algorithm includes a wide class of iterative algorithms, and two special cases of them are studied in detail in this paper. Necessary and sufficient conditions guaranteeing the convergence of the proposed algorithms are presented. Sufficient conditions that are easy to compute are also given. The optimal step sizes such that the convergence rates of the algorithms, which are properly defined in this paper, are maximized and established. Several special cases of the weighted least squares problem, such as a least squares solution to the coupled Sylvester matrix equations problem, solutions to the general coupled Sylvester matrix equations problem, and a weighted least squares solution to the linear matrix equation problem are simultaneously solved. Several numerical examples are given to illustrate the effectiveness of the proposed algorithms. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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8. An algorithm for semi-infinite transportation problems
- Author
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Chen, Shen-Yu and Wu, Soon-Yi
- Subjects
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TRANSPORTATION problems (Programming) , *LINEAR programming , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we consider a class of semi-infinite transportation problems. We develop an algorithm for this class of semi-infinite transportation problems. The algorithm is a primal dual method which is a generalization of the classical algorithm for finite transportation problems. The most important aspect of our paper is that we can prove the convergence result for the algorithm. Finally, we implement some examples to illustrate our algorithm. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
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9. Global LSMR(Gl-LSMR) method for solving general linear systems with several right-hand sides.
- Author
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Mojarrab, M. and Toutounian, F.
- Subjects
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LINEAR systems , *ALGORITHMS , *FINITE volume method , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
The global solvers are an attractive class of iterative solvers for solving linear systems with multiple right-hand sides. In this paper, first, a new global method for solving general linear systems with several right-hand sides is presented. This method is the global version of the LSMR algorithm presented by Fong and Saunders (2011). Then, some theoretical properties of the new method are discussed. Finally, numerical experiments from real applications are used to confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
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10. A regularized sampling algorithm for reconstructing non-bandlimited signals.
- Author
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Chen, Weidong
- Subjects
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MATHEMATICAL regularization , *STATISTICAL sampling , *ALGORITHMS , *SIGNAL processing , *ERROR analysis in mathematics , *MATHEMATICAL analysis - Abstract
In this paper the reconstruction of non-bandlimited sampling is discussed and a regularized sampling algorithm for non-bandlimited signals is presented. The error of the regularized sampling algorithm is presented and compared with the previous algorithm based on Shannon’s sampling theorem and compared with the Tikhonov regularization method in the noisy case. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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11. 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
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12. Almost strictly totally negative matrices: An algorithmic characterization.
- Author
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Alonso, Pedro, Peña, J.M., and Serrano, María Luisa
- Subjects
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MATRICES (Mathematics) , *ALGORITHMS , *MATHEMATICAL analysis , *ELIMINATION (Mathematics) , *REAL numbers - Abstract
A real matrix A = ( a i j ) 1 ≤ i , j , ≤ n is said to be almost strictly totally negative if it is almost strictly sign regular with signature ε = ( − 1 , − 1 , … , − 1 ) , which is equivalent to the property that all its nontrivial minors are negative. In this paper an algorithmic characterization of nonsingular almost strictly totally negative matrices is presented. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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13. 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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14. A paraxial asymptotic model for the coupled Vlasov–Maxwell problem in electromagnetics.
- Author
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Assous, F. and Chaskalovic, J.
- Subjects
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VLASOV equation , *MAXWELL equations , *ELECTROMAGNETISM , *ALGORITHMS , *PROBLEM solving , *MATHEMATICAL analysis - Abstract
Abstract: The time-dependent Vlasov–Maxwell equations are one of the most complete mathematical equations that model charged particle beams or plasma physics problems. However, the numerical solution of this system often requires a large computational effort. It is worthwhile, whenever possible, to take into account the geometrical or physical particularities of the problem to derive asymptotic simpler approximate models, leading to cheaper simulations. In this paper, we consider the case of high energy short beams, as for example the transport of a bunch of highly relativistic charged particles in the interior of a perfectly conducting hollow tube. We then derive and analyze a new paraxial asymptotic model, that approximates the Vlasov–Maxwell equations and is fourth order accurate with respect to a small parameter which reflects the physical characteristics of the problem. This approach promises to be very powerful in its ability to get an accurate and fast algorithm, easy to be developed. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
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15. Arbitrary-level hanging nodes for adaptive -FEM approximations in 3D.
- Author
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Kus, Pavel, Solin, Pavel, and Andrs, David
- Subjects
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ARBITRARY constants , *FINITE element method , *APPROXIMATION theory , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods ( -FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
16. The inverse eigenproblem with a submatrix constraint and the associated approximation problem for -symmetric matrices.
- Author
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Yin, Feng, Guo, Ke, Huang, Guangxin, and Huang, Bormin
- Subjects
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APPROXIMATION theory , *SYMMETRIC matrices , *PROBLEM solving , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: Let and be nontrivial involutions, i.e., and . A matrix is called -symmetric if . This paper presents a -symmetric matrix solution to the inverse eigenproblem with a leading principal submatrix constraint. The solvability condition of the constrained inverse eigenproblem is also derived. The existence, the uniqueness and the expression of the -symmetric matrix solution to the best approximation problem of the constrained inverse eigenproblem are achieved, respectively. An algorithm is presented to compute the -symmetric matrix solution to the best approximation problem. Two numerical examples are given to illustrate the effectiveness of our results. [Copyright &y& Elsevier]
- Published
- 2014
- Full Text
- View/download PDF
17. A note on the dynamic analysis using the generalized finite difference method.
- Author
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Gavete, L., Ureña, F., Benito, J.J., and Salete, E.
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FINITE difference method , *GENERALIZATION , *PROBLEM solving , *ALGORITHMS , *MATHEMATICAL analysis , *STABILITY theory - Abstract
Abstract: This paper shows the application of the generalized finite difference method (GFDM) to the problem of dynamic analysis of beams and plates. The stability conditions for a fully explicit algorithm are given for beams and plates. Measures of the irregularity of the clouds of points for beams and plates are given. Various cases of vibrations of beams and plates have been solved and the results show the accuracy of the method for irregular clouds of nodes. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
18. Spectral binomial tree: New algorithms for pricing barrier options.
- Author
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Muroi, Yoshifumi and Yamada, Takashi
- Subjects
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ALGORITHMS , *OPTIONS (Finance) , *PRICING , *MATHEMATICAL expansion , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
Abstract: This paper introduces new and significantly fast algorithms to evaluate the price of double barrier options using binomial trees. To compute the price of double barrier options accurately, trees with large numbers of steps must be used, which is time consuming. In order to overcome this weakness, we develop new computational algorithms based on the spectral expansion method. The original idea of this method is coming from the eigenexpansion approach in PDEs. We show that this method enables us to compute double barrier options within 0.07 s, even if we use binomial trees with one billion steps. Moreover, this algorithm is easy to implement. In addition, the prices obtained by the proposed approach are always the same as those obtained by conventional binomial trees and show a good approximation to those by earlier studies. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
19. Accurate solution of dense linear systems, Part II: Algorithms using directed rounding
- Author
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Rump, Siegfried M.
- Subjects
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LINEAR systems , *ALGORITHMS , *ERROR analysis in mathematics , *MATHEMATICAL bounds , *MATHEMATICAL analysis - Abstract
Abstract: In Part I and this Part II of our paper we investigate how extra-precise evaluation of dot products can be used to solve ill-conditioned linear systems rigorously and accurately. In Part I only rounding to nearest is used. In this Part II we improve the results significantly by permitting directed rounding. Linear systems with tolerances in the data are treated, and a comfortable way is described to compute error bounds for extremely ill-conditioned linear systems with condition numbers up to about , where denotes the relative rounding error unit in a given working precision. We improve a method by Hansen/Bliek/Rohn/Ning/Kearfott/Neumaier. Of the known methods by Krawczyk, Rump, Hansen et al., Ogita and Nguyen we show that our presented Algorithm LssErrBnd seems the best compromise between accuracy and speed. Moreover, for input data with tolerances, a new method to compute componentwise inner bounds is presented. For not too wide input data they demonstrate that the computed inclusions are often almost optimal. All algorithms are given in executable Matlab code and are available from my homepage. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
20. A modified homotopy perturbation method for solving the nonlinear mixed Volterra–Fredholm integral equation
- Author
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Dong, Chunhuan, Chen, Zhong, and Jiang, Wei
- Subjects
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HOMOTOPY theory , *PERTURBATION theory , *NUMERICAL solutions to nonlinear integral equations , *STOCHASTIC convergence , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: The purpose of this paper is to obtain the approximation solution of the strongly nonlinear mixed Volterra–Fredholm integral equation (VFIE). For some strongly nonlinear problems, the traditional homotopy perturbation method is divergent, so we propose a modified homotopy perturbation method which is still convergent when solving the strongly nonlinear mixed VFIE. By means of this method, an algorithm is successfully established for solving the strongly nonlinear mixed VFIE. And the convergence of the algorithm is proved strictly. Finally, several examples are presented to illustrate the application of the algorithm. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
21. An algorithm for computing a Padé approximant with minimal degree denominator
- Author
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Ibryaeva, O.L. and Adukov, V.M.
- Subjects
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ALGORITHMS , *APPROXIMATION theory , *KERNEL functions , *TOEPLITZ matrices , *TOPOLOGICAL degree , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, a new definition of a reduced Padé approximant and an algorithm for its computation are proposed. Our approach is based on the investigation of the kernel structure of the Toeplitz matrix. It is shown that the reduced Padé approximant always has nice properties which the classical Padé approximant possesses only in the normal case. The new algorithm allows us to avoid the appearance of Froissart doublets induced by computer roundoff in the non-normal Padé table. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
22. Linear bilevel programming with interval coefficients
- Author
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Calvete, Herminia I. and Galé, Carmen
- Subjects
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LINEAR programming , *INTERVAL analysis , *ALGEBRAIC functions , *PROOF theory , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we address linear bilevel programs when the coefficients of both objective functions are interval numbers. The focus is on the optimal value range problem which consists of computing the best and worst optimal objective function values and determining the settings of the interval coefficients which provide these values. We prove by examples that, in general, there is no precise way of systematizing the specific values of the interval coefficients that can be used to compute the best and worst possible optimal solutions. Taking into account the properties of linear bilevel problems, we prove that these two optimal solutions occur at extreme points of the polyhedron defined by the common constraints. Moreover, we develop two algorithms based on ranking extreme points that allow us to compute them as well as determining settings of the interval coefficients which provide the optimal value range. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
23. 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
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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
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24. Relations among eigenvalues of left-definite Sturm–Liouville problems with coupled BCS and separated BCS
- Author
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Zhang, YanXia and Zhang, Xuefeng
- Subjects
- *
EIGENVALUES , *NUMERICAL solutions to Sturm-Liouville equations , *BOUNDARY value problems , *ALGORITHMS , *MATHEMATICAL analysis , *APPLIED mathematics - Abstract
Abstract: This paper deals with Left-Definite regular self-adjoint SLPs with coupled boundary conditions. It is obtained that, for a given eigenvalue of Left-Definite regular SLPs with coupled BCs, there are some separated BCs also having as an eigenvalue with the same index or indices. And then we can construct an algorithm for computing the index of a given eigenvalue for the Left-Definite SLPs with coupled boundary conditions. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
25. A quasi-linear algorithm for calculating the infimal convolution of convex quadratic functions
- Author
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Bayón, L., Grau, J.M., Ruiz, M.M., and Suárez, P.M.
- Subjects
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QUASILINEARIZATION , *ALGORITHMS , *CONVEX functions , *MATHEMATICAL convolutions , *QUADRATIC programming , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we present an algorithm of quasi-linear complexity to exactly calculate the infimal convolution of convex quadratic functions. The algorithm exactly and simultaneously solves a separable uniparametric family of quadratic programming problems resulting from varying the equality constraint. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
26. 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
27. A full-Newton step non-interior continuation algorithm for a class of complementarity problems
- Author
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Zhao, Jian-Xun and Wang, Yong
- Subjects
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ALGORITHMS , *STOCHASTIC convergence , *MATHEMATICAL variables , *MATHEMATICAL analysis , *NONLINEAR theories , *MATHEMATICAL proofs - Abstract
Abstract: In this paper, we investigate a class of nonlinear complementarity problems arising from the discretization of the free boundary problem, which was recently studied by Sun and Zeng [Z. Sun, J. Zeng, A monotone semismooth Newton type method for a class of complementarity problems, J. Comput. Appl. Math. 235 (5) (2011) 1261–1274]. We propose a new non-interior continuation algorithm for solving this class of problems, where the full-Newton step is used in each iteration. We show that the algorithm is globally convergent, where the iteration sequence of the variable converges monotonically. We also prove that the algorithm is globally linearly and locally superlinearly convergent without any additional assumption, and locally quadratically convergent under suitable assumptions. The preliminary numerical results demonstrate the effectiveness of the proposed algorithm. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
28. Detecting discontinuity points from spectral data with the quotient-difference (qd) algorithm
- Author
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Allouche, Hassane, Ghanou, Noura, and Tigma, Khalid
- Subjects
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SPECTRAL theory , *DIFFERENCE equations , *ALGORITHMS , *SMOOTHNESS of functions , *FOURIER analysis , *MATHEMATICAL analysis - Abstract
Abstract: This paper introduces a new technique for the localization of discontinuity points from spectral data. Through this work, we will be able to detect discontinuity points of a -periodic piecewise smooth function from its Fourier coefficients. This could be useful in detecting edges and reducing the effects of the Gibbs phenomenon which appears near discontinuities and affects signal restitution. Our approach consists in moving from a discontinuity point detection problem to a pole detection problem, then adapting the quotient-difference (qd) algorithm in order to detect those discontinuity points. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
29. A fast algorithm for the multivariate Birkhoff interpolation problem
- Author
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Lei, Na, Chai, Junjie, Xia, Peng, and Li, Ying
- Subjects
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INTERPOLATION , *ALGORITHMS , *MULTIVARIATE analysis , *POLYNOMIALS , *COMBINATORICS , *LINEAR systems , *MATHEMATICAL analysis - Abstract
Abstract: Multivariate Birkhoff interpolation is the most complicated polynomial interpolation problem and the theory about it is far from systematic and complete. In this paper we derive an Algorithm B-MB (Birkhoff-Monomial Basis) and prove B-MB giving the minimal interpolation monomial basis w.r.t. the lexicographical order of the multivariate Birkhoff problem. This algorithm is the generalization of Algorithm MB in [L. Cerlinco, M. Mureddu, From algebraic sets to monomial linear bases by means of combinatorial algorithms, Discrete Math. 139 (1995) 73–87] which is a well known fast algorithm used to compute the interpolation monomial basis of the Hermite interpolation problem. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
30. Application of fuzzy soft set in decision making problems based on grey theory
- Author
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Kong, Zhi, Wang, Lifu, and Wu, Zhaoxia
- Subjects
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FUZZY sets , *DECISION making , *ALGORITHMS , *MATHEMATICAL analysis , *FUZZY systems - Abstract
Abstract: There are many uncertain problems in practical production and life which need decisions made with soft sets and fuzzy soft sets. However, the basis of evaluation of the decision method is single and simple, the same decision problem can obtain different results from using a different evaluation basis. In this paper, in order to obtain the right result, we discuss fuzzy soft set decision problems. A new algorithm based on grey relational analysis is presented. The evaluation bases of the new algorithm are multiple. There is more information in a decision result based on multiple evaluation bases, which is more easily accepted and logical to one’s thinking. For the two cases examined, the results show that the new algorithm is efficient for solving decision problems. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
31. A Fitzpatrick algorithm for multivariate rational interpolation
- Author
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Xia, Peng, Zhang, Shugong, and Lei, Na
- Subjects
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MULTIVARIATE analysis , *ALGORITHMS , *INTERPOLATION , *GROBNER bases , *MATHEMATICAL analysis , *CAUCHY problem - Abstract
Abstract: In this paper, we first apply the Fitzpatrick algorithm to osculatory rational interpolation. Then based on a Fitzpatrick algorithm, we present a Neville-like algorithm for Cauchy interpolation. With this algorithm, we can determine the value of the interpolating function at a single point without computing the rational interpolating function. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
32. A modified SLP algorithm and its global convergence
- Author
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Huang, Aiqun, Xu, Chengxian, and Wang, Meihua
- Subjects
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LINEAR programming , *ALGORITHMS , *STOCHASTIC convergence , *NONLINEAR programming , *FILTERS (Mathematics) , *MATHEMATICAL inequalities , *MATHEMATICAL analysis , *CONSTRAINTS (Physics) - Abstract
Abstract: This paper concerns a filter technique and its application to the trust region method for nonlinear programming (NLP) problems. We used our filter trust region algorithm to solve NLP problems with equality and inequality constraints, instead of solving NLP problems with just inequality constraints, as was introduced by Fletcher et al. [R. Fletcher, S. Leyffer, Ph.L. Toint, On the global converge of an SLP-filter algorithm, Report NA/183, Department of Mathematics, Dundee University, Dundee, Scotland, 1999]. We incorporate this filter technique into the traditional trust region method such that the new algorithm possesses nonmonotonicity. Unlike the tradition trust region method, our algorithm performs a nonmonotone filter technique to find a new iteration point if a trial step is not accepted. Under mild conditions, we prove that the algorithm is globally convergent. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
33. IGAOR and multisplitting IGAOR methods for linear complementarity problems
- Author
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Li, Sheng-Guo, Jiang, Hao, Cheng, Li-Zhi, and Liao, Xiang-Ke
- Subjects
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STOCHASTIC convergence , *LINEAR complementarity problem , *NUMERICAL analysis , *MATHEMATICAL analysis , *ALGORITHMS , *PROBLEM solving - Abstract
Abstract: In this paper, we propose an interval version of the generalized accelerated overrelaxation methods, which we refer to as IGAOR, for solving the linear complementarity problems, LCP (M, q), and develop a class of multisplitting IGAOR methods which can be easily implemented in parallel. In addition, in regards to the H-matrix with positive diagonal elements, we prove the convergence of these algorithms and illustrate their efficiency through our numerical results. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
34. Analysis and algorithms for the computation of the excited states of helium
- Author
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Ding, Zhonghai and Chen, Goong
- Subjects
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ALGORITHMS , *HELIUM , *EXCITED state chemistry , *MATHEMATICAL analysis , *COMPARATIVE studies , *SCHRODINGER equation - Abstract
Abstract: In this paper, we study a dimensionally scaled helium atom model for excited states of helium. The mathematical analysis of the corresponding effective energy potential is presented. Two simple numerical algorithms are developed for the computation of the excited states of helium. Comparison between our numerical results and those in the existing literature is given to indicate the accuracy and efficiency of the proposed algorithms. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
35. Improved Hessian approximation with modified secant equations for symmetric rank-one method
- Author
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Modarres, Farzin, Malik, Abu Hassan, and Leong, Wah June
- Subjects
- *
APPROXIMATION theory , *ALGORITHMS , *NUMERICAL analysis , *MATHEMATICAL symmetry , *MATHEMATICAL analysis , *NUMERICAL solutions to equations - Abstract
Abstract: Symmetric rank-one (SR1) is one of the competitive formulas among the quasi-Newton (QN) methods. In this paper, we propose some modified SR1 updates based on the modified secant equations, which use both gradient and function information. Furthermore, to avoid the loss of positive definiteness and zero denominators of the new SR1 updates, we apply a restart procedure to this update. Three new algorithms are given to improve the Hessian approximation with modified secant equations for the SR1 method. Numerical results show that the proposed algorithms are very encouraging and the advantage of the proposed algorithms over the standard SR1 and BFGS updates is clearly observed. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
36. An efficient linearization technique for mixed 0–1 polynomial problem
- Author
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Ghezavati, V.R. and Saidi-Mehrabad, M.
- Subjects
- *
POLYNOMIALS , *BOUNDARY value problems , *MATHEMATICAL variables , *ALGORITHMS , *MATHEMATICAL analysis , *NUMBER theory - Abstract
Abstract: This paper addresses a new and efficient linearization technique to solve mixed 0–1 polynomial problems to achieve a global optimal solution. Given a mixed 0–1 polynomial term , where are binary (0–1) variables and is a continuous variable. Also, can be either a positive or a negative parameter. We transform into a set of auxiliary constraints which are linear and can be solved by exact methods such as branch and bound algorithms. For this purpose, we will introduce a method in which the number of additional constraints is decreased significantly rather than the previous methods proposed in the literature. As is known in any operations research problem decreasing the number of constraints leads to decreasing the mathematical computations, extensively. Thus, research on the reducing number of constraints in mathematical problems in complicated situations have high priority for decision makers. In this method, each -auxiliary constraints proposed in the last method in the literature for the linearization problem will be replaced by only 3 novel constraints. In other words, previous methods were dependent on the number of 0–1 variables and therefore, one auxiliary constraint was considered per 0–1 variable, but this method is completely independent of the number of 0–1 variables and this illustrates the high performance of this method in computation considerations. The analysis of this method illustrates the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
37. Finding DEA-efficient hyperplanes using MOLP efficient faces
- Author
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Lotfi, F. Hosseinzadeh, Jahanshahloo, G.R., Mozaffari, M.R., and Gerami, J.
- Subjects
- *
DATA envelopment analysis , *LINEAR programming , *PLANE geometry , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: This paper suggests a method for finding efficient hyperplanes with variable returns to scale the technology in data envelopment analysis (DEA) by using the multiple objective linear programming (MOLP) structure. By presenting an MOLP problem for finding the gradient of efficient hyperplanes, We characterize the efficient faces. Thus, without finding the extreme efficient points of the MOLP problem and only by identifying the efficient faces of the MOLP problem, we characterize the efficient hyperplanes which make up the DEA efficient frontier. Finally, we provide an algorithm for finding the efficient supporting hyperplanes and efficient defining hyperplanes, which uses only one linear programming problem. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
38. GBi-CGSTAB(): IDR() with higher-order stabilization polynomials
- Author
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Tanio, Masaaki and Sugihara, Masaaki
- Subjects
- *
POLYNOMIALS , *ITERATIVE methods (Mathematics) , *LINEAR systems , *ALGORITHMS , *TOPOLOGICAL spaces , *MATHEMATICAL analysis - Abstract
Abstract: IDR() is now recognized as one of the most effective methods, often superior to other Krylov subspace methods, for large nonsymmetric linear systems of equations. In this paper we propose an improvement upon IDR() by incorporating a higher-order stabilization polynomial into IDR(). The proposed algorithm, named GBi-CGSTAB(), shares desirable features with both IDR() and Bi-CGSTAB(). [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
39. An efficient computational method for linear fifth-order two-point boundary value problems
- Author
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Lv, Xueqin and Cui, Minggen
- Subjects
- *
COMPUTATIONAL complexity , *BOUNDARY value problems , *LINEAR statistical models , *ALGORITHMS , *KERNEL functions , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we present a new algorithm to solve general linear fifth-order boundary value problems (BVPs) in the reproducing kernel space . Representation of the exact solution is given in the reproducing kernel space. Its approximate solution is obtained by truncating the -term of the exact solution. Some examples are displayed to demonstrate the computational efficiency of the method. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
40. A non-interior-point smoothing method for variational inequality problem
- Author
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Zhang, Xiangsong, Liu, Sanyang, and Liu, Zhenhua
- Subjects
- *
SMOOTHING (Numerical analysis) , *VARIATIONAL inequalities (Mathematics) , *ALGORITHMS , *STOCHASTIC convergence , *LINEAR complementarity problem , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we focus on the variational inequality problem. Based on the Fischer–Burmeister function with smoothing parameters, the variational inequality problem can be reformulated as a system of parameterized smooth equations, a non-interior-point smoothing method is presented for solving the problem. The proposed algorithm not only has no restriction on the initial point, but also has global convergence and local quadratic convergence, moreover, the local quadratic convergence is established without a strict complementarity condition. Preliminary numerical results show that the algorithm is promising. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
41. A branch and reduce approach for solving a class of low rank d.c. programs
- Author
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Cambini, Riccardo and Salvi, Francesca
- Subjects
- *
MATHEMATICAL programming , *MATHEMATICAL literature , *PARTITIONS (Mathematics) , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: Various classes of d.c. programs have been studied in the recent literature due to their importance in applicative problems. In this paper we consider a branch and reduce approach for solving a class of d.c. problems. Seven partitioning rules are analyzed and some techniques aimed at improving the overall performance of the algorithm are proposed. The results of a computational experience are provided in order to point out the performance effectiveness of the proposed techniques. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
42. Fast reconstruction of aerodynamic shapes using evolutionary algorithms and virtual nash strategies in a CFD design environment
- Author
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Periaux, J., Lee, D.S., Gonzalez, L.F., and Srinivas, K.
- Subjects
- *
ALGORITHMS , *COMPUTER software , *COMPUTATIONAL fluid dynamics , *AERODYNAMICS , *MATHEMATICAL optimization , *GAME theory , *MATHEMATICAL analysis - Abstract
Abstract: This paper compares the performances of two different optimisation techniques for solving inverse problems; the first one deals with the Hierarchical Asynchronous Parallel Evolutionary Algorithms software (HAPEA) and the second is implemented with a game strategy named Nash-EA. The HAPEA software is based on a hierarchical topology and asynchronous parallel computation. The Nash-EA methodology is introduced as a distributed virtual game and consists of splitting the wing design variables–aerofoil sections–supervised by players optimising their own strategy. The HAPEA and Nash-EA software methodologies are applied to a single objective aerodynamic ONERA M6 wing reconstruction. Numerical results from the two approaches are compared in terms of the quality of model and computational expense and demonstrate the superiority of the distributed Nash-EA methodology in a parallel environment for a similar design quality. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
43. A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition
- Author
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Slodička, Marián and Dehilis, Sofiane
- Subjects
- *
NUMERICAL solutions to parabolic differential equations , *BOUNDARY value problems , *ERROR analysis in mathematics , *ALGORITHMS , *FINITE element method , *ITERATIVE methods (Mathematics) , *MATHEMATICAL analysis - Abstract
Abstract: A semilinear reaction-diffusion problem with a nonlocal boundary condition is studied. This paper presents a new and very easy implementable numerical algorithm for computations. This is based on a suitable linearization in time and on the principle of linear superposition. Any method for the space discretization (FEM was taken in this analysis) can be chosen. The derived algorithm is implicit and it does not need any iteration scheme to get a solution with the nonlocal boundary condition. Stability analysis has been performed and the optimal error estimates have been derived. Numerical results have been compared with other known techniques. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
44. A two-dimensional matrix Padé-type approximation in the inner product space
- Author
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Tao, Youtian and Gu, Chuanqing
- Subjects
- *
PADE approximant , *APPROXIMATION theory , *MATRICES (Mathematics) , *LINEAR systems , *ALGORITHMS , *INNER product spaces , *POLYNOMIALS , *MATHEMATICAL analysis - Abstract
Abstract: By introducing a bivariate matrix-valued linear functional on the scalar polynomial space, a general two-dimensional (2-D) matrix Padé-type approximant () in the inner product space is defined in this paper. The coefficients of its denominator polynomials are determined by taking the direct inner product of matrices. The remainder formula is developed and an algorithm for the numerator polynomials is presented when the generating polynomials are given in advance. By means of the Hankel-like coefficient matrix, a determinantal expression of is presented. Moreover, to avoid the computation of the determinants, two efficient recursive algorithms are proposed. At the end the method of is applied to partial realization problems of 2-D linear systems. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
45. Assessing the lifetime performance index of products with the exponential distribution under progressively type II right censored samples
- Author
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Lee, Wen-Chuan, Wu, Jong-Wuu, and Hong, Ching-Wen
- Subjects
- *
PRODUCT life cycle , *MAXIMUM likelihood statistics , *DISTRIBUTION (Probability theory) , *STATISTICAL hypothesis testing , *ALGORITHMS , *MATHEMATICAL analysis - Abstract
Abstract: In practice, lifetime performance index is used to measure the potential and performance of a process, where is the lower specification limit. Progressive censoring scheme is quite useful in many practical situations where budget constraints are in place or there is a demand for rapid testing. In this paper, under the assumption of exponential distribution, this study constructs a maximum likelihood estimator (MLE) of based on the progressively type II right censored sample. The MLE of is then utilized to develop the hypothesis testing procedure in the condition of known . The new testing procedure can be employed by product managers to assess whether the lifetime of products (or items) adheres to the required level in the condition of known . Finally, we give one example to illustrate the use of the testing algorithmic procedure under given significance level. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
46. A fuzzy shortest path with the highest reliability
- Author
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Keshavarz, Esmaile and Khorram, Esmaile
- Subjects
- *
FUZZY decision making , *NONLINEAR programming , *MAXIMA & minima , *MATHEMATICAL analysis , *ALGORITHMS , *STATISTICAL reliability - Abstract
Abstract: This paper concentrates on a shortest path problem on a network where arc lengths (costs) are not deterministic numbers, but imprecise ones. Here, costs of the shortest path problem are fuzzy intervals with increasing membership functions, whereas the membership function of the total cost of the shortest path is a fuzzy interval with a decreasing linear membership function. By the max–min criterion suggested in [R.E. Bellman, L.A. Zade, Decision-making in a fuzzy environment, Management Science 17B (1970) 141–164], the fuzzy shortest path problem can be treated as a mixed integer nonlinear programming problem. We show that this problem can be simplified into a bi-level programming problem that is very solvable. Here, we propose an efficient algorithm, based on the parametric shortest path problem for solving the bi-level programming problem. An illustrative example is given to demonstrate our proposed algorithm. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
47. Condition number based complexity estimate for computing local extrema
- Author
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She, Zhikun and Zheng, Zhiming
- Subjects
- *
ALGORITHMS , *EXTREMAL problems (Mathematics) , *METHOD of steepest descent (Numerical analysis) , *APPROXIMATION theory , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we present a new algorithm for computing local extrema by modifying and combining algorithms in symbolic and numerical computation. This new algorithm improves the classical steepest descent method that may not terminate, by combining a Sturm’s theorem based separation method and a sufficient condition on infeasibility. In addition, we incorporate a grid subdivision method into our algorithm to approximate all local extrema. The complexity of our algorithm is polynomial in a newly defined condition number, and singly exponential in the number of variables. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
48. Properties of a family of generalized NCP-functions and a derivative free algorithm for complementarity problems
- Author
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Hu, Sheng-Long, Huang, Zheng-Hai, and Chen, Jein-Shan
- Subjects
- *
MATHEMATICAL functions , *MATHEMATICAL programming , *ALGORITHMS , *NONLINEAR theories , *LIPSCHITZ spaces , *STOCHASTIC convergence , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we propose a new family of NCP-functions and the corresponding merit functions, which are the generalization of some popular NCP-functions and the related merit functions. We show that the new NCP-functions and the corresponding merit functions possess a system of favorite properties. Specially, we show that the new NCP-functions are strongly semismooth, Lipschitz continuous, and continuously differentiable; and that the corresponding merit functions have property (i.e., they are continuously differentiable and their gradients are semismooth) and property (i.e., they are continuously differentiable and their gradients are Lipschitz continuous) under suitable assumptions. Based on the new NCP-functions and the corresponding merit functions, we investigate a derivative free algorithm for the nonlinear complementarity problem and discuss its global convergence. Some preliminary numerical results are reported. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
49. On some explicit Adams multistep methods for fractional differential equations
- Author
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Garrappa, Roberto
- Subjects
- *
NUMERICAL solutions to differential equations , *FRACTIONAL calculus , *MATHEMATICAL formulas , *NUMERICAL analysis , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
Abstract: In this paper we present a family of explicit formulas for the numerical solution of differential equations of fractional order. The proposed methods are obtained by modifying, in a suitable way, Fractional-Adams–Moulton methods and they represent a way for extending classical Adams–Bashforth multistep methods to the fractional case. The attention is hence focused on the investigation of stability properties. Intervals of stability for -step methods, , are computed and plots of stability regions in the complex plane are presented. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
50. A smoothing method for second order cone complementarity problem
- Author
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Zhang, Xiangsong, Liu, Sanyang, and Liu, Zhenhua
- Subjects
- *
SMOOTHING (Numerical analysis) , *PERTURBATION theory , *STOCHASTIC convergence , *NEWTON-Raphson method , *MATHEMATICAL analysis , *ALGORITHMS , *MATHEMATICAL reformulation - Abstract
Abstract: In this paper, the second order cone complementarity problem is studied. Based on a perturbed symmetrically smoothing function, which has coerciveness under proper conditions, we present a smoothing Newton method for this problem. The boundedness of the level set can be obtained from the coerciveness, which plays an important role in the convergence analysis. Furthermore, the proposed algorithm for the reformulation has no restrictions on the starting point and solves only one system of equations. Preliminary numerical results indicate that the algorithm is effective. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
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