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Reducing a Matrix to Hessenberg Form

P. A. Businger
Mathematics of Computation
Vol. 23, No. 108 (Oct., 1969), pp. 819-821
DOI: 10.2307/2004967
Stable URL: http://www.jstor.org/stable/2004967
Page Count: 3
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Reducing a Matrix to Hessenberg Form
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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.

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