Accelerating the Induced Dimension Reduction method using spectral information

R. Astudillo; J.M. de Gier; M. B. van Gijzen

doi:10.1016/j.cam.2018.06.014

Accelerating the Induced Dimension Reduction method using spectral information

R. Astudillo , J.M. de Gier, M. B. van Gijzen

Numerical Analysis

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Abstract

The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations.

Original language	English
Pages (from-to)	33-47
Number of pages	15
Journal	Journal of Computational and Applied Mathematics
Volume	345
DOIs	https://doi.org/10.1016/j.cam.2018.06.014
Publication status	Published - 2019

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

Keywords

Eigenvalues and eigenvectors
Induced Dimension Reduction method
Sequence of systems of linear equation
System of linear equations

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10.1016/j.cam.2018.06.014

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title = "Accelerating the Induced Dimension Reduction method using spectral information",

abstract = "The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations.",

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note = "Green Open Access added to TU Delft Institutional Repository {\textquoteleft}You share, we take care!{\textquoteright} – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. ",

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AU - de Gier, J.M.

AU - van Gijzen, M. B.

N1 - Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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N2 - The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations.

AB - The Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations.

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KW - Induced Dimension Reduction method

KW - Sequence of systems of linear equation

KW - System of linear equations

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JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

Accelerating the Induced Dimension Reduction method using spectral information

Abstract

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Keywords

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