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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Computing invariant subspaces of a general matrix when the eigensystem is poorly conditioned
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by J. M. Varah PDF
Math. Comp. 24 (1970), 137-149 Request permission


The problem of calculating the eigensystem of a general complex matrix is well known. In many cases, however, the eigensystem is poorly determined numerically in the sense that small changes in the matrix can cause large changes in the eigensystem. For these matrices, a decomposition into higher-dimensional invariant subspaces is desirable. In this paper we define a class of matrices where this is true, and propose a technique for calculating bases for these invariant subspaces. We show that for this class the technique provides basis vectors which are accurate and span the subspaces well.
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 137-149
  • MSC: Primary 65.40
  • DOI:
  • MathSciNet review: 0264843