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Zbl 0759.15016
Robinson, P.D.; Wathen, A.J.
Variational bounds on the entries of the inverse of a matrix. (English)
[J] IMA J. Numer. Anal. 12, No.4, 463-486 (1992). ISSN 0272-4979; ISSN 1464-3642/e

Variational (and bivariational) techniques are used to derive bounds on the entries of the inverse of a nonsingular matrix. These bounds involve the extreme eigenvalues or singular values of the matrix. Direct variational bounding techniques for linear operator equations on a Hilbert space and also for finite-dimensional Euclidean spaces are applied. Examples and comparisons using polynomial inequalities for stationary points (finite values) using classical inequalities are given. The nonsymmetric case is also investigated.
[D.Voukalis (Athens)]

MSC 2000:: *15A45 Miscellaneous inequalities involving matrices
15A09 Matrix inversion

Keywords: entries of the inverse; real non-singular matrix; non-symmetric; Kantorovich inequality; Rayleigh quotient; variational bounds; bivariational bound; Wielandt inequality

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