Block-Toeplitz preconditioning for static and dynamic linear systems

K. Burrage; Zdzislaw Jackiewicz; Bruno Welfert

doi:10.1016/S0024-3795(98)00007-X

Block-Toeplitz preconditioning for static and dynamic linear systems

K. Burrage, Zdzislaw Jackiewicz, Bruno Welfert

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.

Original language	English (US)
Pages (from-to)	51-74
Number of pages	24
Journal	Linear Algebra and Its Applications
Volume	279
Issue number	1-3
DOIs	https://doi.org/10.1016/S0024-3795(98)00007-X
State	Published - Aug 15 1998

Keywords

Accelerating of convergence
Iterative methods
Overlapping
Preconditioning
Splitting
Waveform relaxation method

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/S0024-3795(98)00007-X

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title = "Block-Toeplitz preconditioning for static and dynamic linear systems",

abstract = "Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.",

keywords = "Accelerating of convergence, Iterative methods, Overlapping, Preconditioning, Splitting, Waveform relaxation method",

author = "K. Burrage and Zdzislaw Jackiewicz and Bruno Welfert",

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T1 - Block-Toeplitz preconditioning for static and dynamic linear systems

AU - Burrage, K.

AU - Jackiewicz, Zdzislaw

AU - Welfert, Bruno

PY - 1998/8/15

Y1 - 1998/8/15

N2 - Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.

AB - Acceleration techniques for iterative methods for linear systems of both static (Qy = b) and dynamic (y′ = Qy + g(t)) type are analyzed. A new splitting Q = M - N, where M is block-Toeplitz is proposed. In the static case considerable improvement is observed, while in the dynamic case this preconditioning results only in a slightly faster waveform relaxation scheme than the traditional block-Jacobi dynamic iteration method in the case of linear systems approximating heat equation in one or two dimensions. It is shown that the static analysis does not predict correctly the optimal value of the parameters introduced for the dynamic case, but that a spectral analysis does.

KW - Accelerating of convergence

KW - Iterative methods

KW - Overlapping

KW - Preconditioning

KW - Splitting

KW - Waveform relaxation method

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