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
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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
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