Accelerating the Induced Dimension Reduction method using spectral information

Report (2017)

Authors

R.A. Astudillo Rengifo Numerical Analysis - EEMCS
M.B. van Gijzen Numerical Analysis - EEMCS
Research Group
Numerical Analysis (EEMCS) (TU Delft)
System of linear equations Induced Dimension Reduction method Sequence of systems of linear equation Eigenvalues and eigenvectors
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Published Date

2017

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)) [1] is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using the 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 [2] for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) in the solution of a sequence of linear systems.

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