Extremal properties of balanced tridiagonal matrices
Author:
Peter A. Businger
Journal:
Math. Comp. 23 (1969), 193195
MSC:
Primary 65.35
MathSciNet review:
0238476
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Abstract: If is a square matrix with distinct eigenvalues and a nonsingular matrix, then the angles between row and columneigenvectors of differ from the corresponding quantities of . Perturbation analysis of the eigenvalue problem motivates the minimization of functions of these angles over the set of diagonal similarity transforms; two such functions which are of particular interest are the spectral and the Euclidean condition numbers of the eigenvector matrix of . It is shown that for a tridiagonal real matrix both these condition numbers are minimized when is chosen such that the magnitudes of corresponding sub and superdiagonal elements are equal.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718196902384766
PII:
S 00255718(1969)02384766
Article copyright:
© Copyright 1969 American Mathematical Society
