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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2004967
Page Count: 3
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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.
Mathematics of Computation © 1969 American Mathematical Society