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Variational bounds on the entries of the inverse of a matrix. (English) Zbl 0759.15016
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.
MSC:
15A45Miscellaneous inequalities involving matrices
15A09Matrix inversion, generalized inverses