Title

Approximating the generalized singular value expansion

Authors

Mark Gockenbach, Michigan Technological UniversityFollow
Matthew J. Roberts, Michigan Technological University

Document Type

Article

Publication Date

9-11-2018

Abstract

The generalized singular value expansion (GSVE) simultaneously diagonalizes a pair of operators on Hilbert space. From a theoretical point of view, the GSVE enables a straightforward analysis of, for example, weighted least-squares problems and the method of Tikhonov regularization with seminorms. When the operators are discretized, an approximate GSVE can be computed from the generalized singular value decomposition of a pair of Galerkin matrices. Unless the discretization is carefully chosen, spurious modes can appear, but a natural condition on the discretization guarantees convergence of the approximate GSVE to the exact one. Numerical examples illustrate the pitfalls of a poor discretization and efficacy of the convergence conditions.

Publisher's Statement

Copyright 2018 Society for Industrial and Applied Mathematics. Article deposited here in compliance with publisher policy. Publisher's version of record: https://doi.org/10.1137/18M1163713

Publication Title

SIAM Journal on Numerical Analysis

Recommended Citation

Gockenbach, M., & Roberts, M. J. (2018). Approximating the generalized singular value expansion. SIAM Journal on Numerical Analysis, 56(5), 2776-2795. http://doi.org/10.1137/18M1163713
Retrieved from: https://digitalcommons.mtu.edu/math-fp/11

Version

Publisher's PDF