An Evaluation of Software for Computing Eigenvalues of Sparse Nonsymmetric Matrices

Abstract

The past few years have seen a signi cant increase in research intonumerical methods for computing selected eigenvalues of large sparse nonsymmetric matrices. This research has begun to lead to the development of high-quality mathematical software. The software includescodes that implement subspace iteration methods, Arnoldi-based algorithms, and nonsymmetric Lanczos methods. The aim of the current study is to evaluate this state-of-the-art software. In this study weconsider subspace iteration and Arnoldi codes. We look at the keyfeatures of the codes and their ease of use. Then, using a wide rangeof test problems, we compare the performance of the codes in termsof storage requirements, execution times, accuracy, and reliability. We also consider their suitability for solving large-scale industrial problems. Based on our ndings, we suggest how improved software shouldbe designed.