Computation of generalized matrix functions

Arrigo, Francesca and Benzi, Michele and Fenu, Caterina (2016) Computation of generalized matrix functions. SIAM Journal on Matrix Analysis and Applications, 37 (3). 836–860. ISSN 0895-4798

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    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