An induced dimension reduction algorithm to approximate eigenpairs of large nonsymmetric matrices

Abstract

Abstract. This work presents an algorithm to approximate eigenpairs of large, sparse and nonsymmetric matrices based on the Induced Dimension Reduction method (IDR(s)) introduced in [1]. We obtain a Hessenberg relation from IDR(s) computations and in conjunction with Implicitly Restarting and shift-and-invert techniques [2] we created a short recurrence algorithm to approximate eigenvalues and its corresponding eigenvectors in a region of interest.

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

“…IDR(s) as a method to compute eigenvalues was first studied by M. H. Gutknecht and J.-P. M. Zemke in [6]. The work we present here is a continuation of [2]. We describe how to obtain an underlying Hessenberg decomposition of the form (2) from IDR(s), and we combine it with the implicitly restarting technique introduced by D.C. Sorensen [22] for Arnoldi in order to approximate eigenpairs of interest.…”