Computation of generalized matrix functions

Arrigo, Francesca;Benzi, Michele;Fenu, Caterina

2016-01-01

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Abstract

We develop numerical algorithms for the efficient evaluation of quantities associated with generalized matrix functions [J. B. Hawkins and A. Ben-Israel, Linear Multilinear Algebra, 1 (1973), pp. 163-171]. Our algorithms are based on Gaussian quadrature and Golub Kahan bidiagonalization. Block variants are also investigated. Numerical experiments are performed to illustrate the effectiveness and efficiency of our techniques in computing generalized matrix functions arising in the analysis of networks.