Abstract
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 XTf(A)Y, where A∈Rp×p is a given diagonalizable matrix, X, Y∈Rp×k 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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
