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

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.