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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Reducing a matrix to Hessenberg form


Author: P. A. Businger
Journal: Math. Comp. 23 (1969), 819-821
MSC: Primary 65.35
MathSciNet review: 0258255
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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 [Enhancements On Off] (What's this?)

  • [1] 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.
  • [2] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965. MR 0184422 (32 #1894)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0258255-3
PII: S 0025-5718(1969)0258255-3
Article copyright: © Copyright 1969 American Mathematical Society