Computation of Generalized Matrix Functions
Francesca Arrigo, Michele Benzi, Caterina Fenu · SIAM Journal on Matrix Analysis and Applications · 2016
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.