An Evaluation of Software for Computing Eigenvalues of Sparse Nonsymmetric Matrices

  • Lehoucq R
  • Scott J
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Abstract

The past few years have seen a signi cant increase in research into
numerical 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 includes
codes 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 we
consider subspace iteration and Arnoldi codes. We look at the key
features of the codes and their ease of use. Then, using a wide range
of test problems, we compare the performance of the codes in terms
of 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 should
be designed.

Author-supplied keywords

  • arnoldi method
  • eigenvalues
  • lanczos method

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Authors

  • R B Lehoucq

  • J a Scott

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