Accelerating the Induced Dimension Reduction method using spectral information

Journal article (2019)

Authors

R.A. Astudillo Rengifo Numerical Analysis - EEMCS
M.B. van Gijzen Numerical Analysis - EEMCS
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Copyright: © 2019 R.A. Astudillo Rengifo, J.M. de Gier, M.B. van Gijzen
DOI
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https://doi.org/10.1016/j.cam.2018.06.014
Eigenvalues and eigenvectors Induced Dimension Reduction method Sequence of systems of linear equation System of linear equations
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Published Date

2019

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

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.