The e-MoM approach for approximating matrix functionals

[摘要] The approximation of matrix functionals appears in many applications arising from the fields of mathematics, statistics, mechanics, networks, machine learning and physics. In this paper, we estimate matrix functionals of the form X(T)f (A)Y, where A is an element of R-pxp is a given diagonalizable matrix, X, Y is an element of R-pxk are skinny block vectors with k << p columns and f is a smooth function defined on the spectrum of the matrix A. We apply a direct approach based on the extrapolation of the moments of the given matrix, for estimating this kind of matrix functionals. This approach avoids the application of the polarization identity, is fairly inexpensive and leads to a stable procedure. Moreover, we develop a detailed backward error analysis for the derived estimates. Several numerical results illustrating the effectiveness of the direct method are presented and concrete classes of matrices, suitable for the extrapolation estimates, are proposed. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2020-08-01

[效力级别]  Proceedings Paper

[关键词] Matrix functionals;Extrapolation;Polarization identity