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arXiv · 1206.1762

On the condition number and perturbation of matrix functions for Hermitian matrices

Elias Jarlebring·Emanuel H. Rubensson
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Abstract

Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation ||f(A+E)-f(A)|| expressed in terms of eigenvalues of A and A+E. The results are general and under certain conditions hold for an arbitrary unitarily invariant matrix norm ||\cdot||. We illustrate the use of the formulas with an application to the error analysis of calculations in electronic structure theory.

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Elias Jarlebring, Emanuel H. Rubensson. 2012-06-08. On the condition number and perturbation of matrix functions for Hermitian matrices. https://arxiv.org/abs/1206.1762

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