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Matrix Pencils pp 121–144Cite as

Projection methods for solving large sparse eigenvalue problems

  • Section A.3 Of General (A-λB)-Pencils
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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 973))

Abstract

We present a unified approach to several methods for computing eigenvalues and eigenvectors of large sparse matrices. The methods considered are projection methods, i.e. Galerkin type methods, and include the most commonly used algorithms for solving large sparse eigenproblems like the Lanczos algorithm, Arnoldi's method and the subspace iteration. We first derive some a priori error bounds for general projection methods, in terms of the distance of the exact eigenvector from the subspace of approximation. Then this distance is estimated for some typical methods, particularly those for unsymmetric problems.

This work was supported in part by the U.S. Office of Naval Research under grant N000014-76-C-0277 and in part by NSF Grant MCS-8104874

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Authors
  1. Youcef Saad
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Bo Kågström Axel Ruhe

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© 1983 Springer-Verlag

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Saad, Y. (1983). Projection methods for solving large sparse eigenvalue problems. In: Kågström, B., Ruhe, A. (eds) Matrix Pencils. Lecture Notes in Mathematics, vol 973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062098

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  • DOI: https://doi.org/10.1007/BFb0062098

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11983-8

  • Online ISBN: 978-3-540-39447-1

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