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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Reducing a matrix to Hessenberg form
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by P. A. Businger PDF
Math. Comp. 23 (1969), 819-821 Request permission

Abstract:

It has been an open problem whether the reduction of a matrix to Hessenberg (almost triangular) form by Gaussian similarity transformations is numerically stable [$2$, p. 364]. We settle this question by exhibiting a class of matrices for which this process is unstable.
References
    J. M. Varah, The Computation of Bounds for the Invariant Subspaces of a General Matrix Operator, Tech. Report No. CS66, Stanford University, Stanford, Calif., 1967.
  • J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422
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Additional Information
  • © Copyright 1969 American Mathematical Society
  • Journal: Math. Comp. 23 (1969), 819-821
  • MSC: Primary 65.35
  • DOI: https://doi.org/10.1090/S0025-5718-1969-0258255-3
  • MathSciNet review: 0258255