A restarted Induced Dimension Reduction method to approximate eigenpairs of large unsymmetric matrices

Journal article (2016)

Authors

R.A. Astudillo Rengifo Numerical Analysis - EEMCS , Universidad Central de Venezuela
M.B. van Gijzen Numerical Analysis - EEMCS
Research Group
Numerical Analysis (EEMCS) (TU Delft)
Induced Dimension Reduction method Eigenpairs approximation Implicitly restarting Polynomial filter
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Published Date

2016

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Numerical Analysis

Abstract

This work presents a new algorithm to compute eigenpairs of large unsymmetric matrices. Using the Induced Dimension Reduction method (IDR(ss)), which was originally proposed for solving systems of linear equations, we obtain a Hessenberg decomposition, from which we approximate the eigenvalues and eigenvectors of a matrix. This decomposition has two main advantages. First, IDR(ss) is a short-recurrence method, which is attractive for large scale computations. Second, the IDR(ss) polynomial used to create this Hessenberg decomposition is also used as a filter to discard the unwanted eigenvalues. Additionally, we incorporate the implicitly restarting technique proposed by D.C. Sorensen, in order to approximate specific portions of the spectrum and improve the convergence.