Accelerating the Induced Dimension Reduction method using spectral information

Accelerating the Induced Dimension Reduction method using spectral information

Astudillo Rengifo, R.A. (TU Delft Numerical Analysis)
de Gier, J.M. (TNO)
van Gijzen, M.B. (TU Delft Numerical Analysis)

2019

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.

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

http://resolver.tudelft.nl/uuid:c7d0bcb1-1ed4-4290-8bd8-5c1391998fbc

https://doi.org/10.1016/j.cam.2018.06.014

2021-11-02

0377-0427

Journal of Computational and Applied Mathematics, 345, 33-47

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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journal article

© 2019 R.A. Astudillo Rengifo, J.M. de Gier, M.B. van Gijzen