Tchebychev acceleration technique for large scale nonsymmetric matrices

Ho, Diem

doi:10.1007/bf01405199

Cited by 17 publications

(25 citation statements)

References 19 publications

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“…Two methods are discussed both from the theoretical and the practical point of view: a block-Arnoldi method and an adaptation of the Davidson method to the unsymmetric case. The former method and some of its variants have been recently studied [7,[11][12][13]. The latter one is very popular in quantum chemistry [4].…”

Section: Introductionmentioning

confidence: 99%

Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

Sadkane

1993

Numer. Math.

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Summary. We present two methods for computing the leading eigenpairs of large sparse unsymmetric matrices. Namely the block-Arnoldi method and an adaptation of the Davidson method to unsymmetric matrices. We give some theoretical results concerning the convergence and discuss implementation aspects of the two methods. Finally some results of numerical tests on a variety of matrices, in which we compare these two methods are reported. Mathematics Subject Classification (1991): 65F 15

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Section: Introductionmentioning

confidence: 99%

Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

Sadkane

1993

Numer. Math.

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“…We have used the algorithm studied by Ho [4] to solve the problem ~'. We will not describe this algorithm in this paper.…”

Section: (D -~) + ((~ -~)~ -C~) I/~mentioning

confidence: 99%

“…One way to overcome this difficulty is to use the real part of the eigenvalues as a reference point [14"1. Ho [4] has developed a new procedure to find the optimal ellipse containing the unwanted eigenvalues without having to verify all possible ellipses. This procedure computes the exact rate of convergence of the Chebyshev ellipse with respect to the eigenvalues in the complex plane.…”

Section: Introductionmentioning

confidence: 99%

A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices

Sadkane

1993

Numer. Math.

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Summary. In this paper we describe a block version of Arnoldi's method for computing a few eigenvalues with largest or smallest real parts. The method is accelerated via Chebyshev iteration and a procedure is developed to identify the optimal ellipse which encloses the spectrum. A parallel implementation of this method is investigated on the eight processor Alliant FX/80. Numerical results and comparisons with simultaneous iteration on some Harwell-Boeing matrices are reported.

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“…Thus, an iterative Arnoldi algorithm with reorthogonalization (Saad 1980) has been developed and seems to work fairly well. Furthermore, acceleration techniques (Saad 1984;Ho 1990) have been developed to speed up the convergence of the Arnoldi algorithm. The standard Arnoldi algorithm does not give approximations to the left eigenvectors of a matrix.…”

Section: 1mentioning

confidence: 99%

ElGENANALYSlS OF LARGE ELECTRIC POWER SYSTEMS

Elwood¹

1991

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SUMMARYModern electric power systems are large and complicated, and, in many regions, the generation and transmission systems are operating near their limits. Eigenanalysis is one of the tools used to analyze the behavior of these systems. Standard eigenvalue methods require that simplified models be used for these analyses; however, these simplified models do not adequately model all of the characteristics of large power systems. Thus, new eigenanalysis methods that can analyze detailed power system models are required.The primary objectives of the work described in this report were I) to determine the availability of eigenanalysis algorithms that are better than methods currently being applied and that could be used an large power systems and 2) to determine if vector supercomputers could be used to significantly increase the size of power systems that can be analyzed by a standard power system eigenanalysis code.At the request of the Bonneville Power Administration, the Pacific Northwest Laboratory (PNL) conducted a literature review of methods currently used for the eigenanalysis of large electric power systems, as well as of general eigenanalysis algorithms that are applicable to large power systems. PNL found that a number of methods are currently being used for the this purpose, and all seem to work fairly well. Furthermore, most of the general eigenanalysis techniques that are applicable to power systems have been tried on these systems, and most seem to work fairly well. One of these techniques, a variation of the Arnoldi method, has been incorporated into a standard power system eigenanalysis package.

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Tchebychev acceleration technique for large scale nonsymmetric matrices

Cited by 17 publications

References 19 publications

Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

Block-Arnoldi and Davidson methods for unsymmetric large eigenvalue problems

A block Arnoldi-Chebyshev method for computing the leading eigenpairs of large sparse unsymmetric matrices

ElGENANALYSlS OF LARGE ELECTRIC POWER SYSTEMS

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