Dissertation/Thesis Abstract

Approximation of the Generalized Singular Value Expansion
by Roberts, Matthew J., Ph.D., Michigan Technological University, 2019, 73; 13863536
Abstract (Summary)

Let X, Y, and Z be real separable Hilbert spaces, let  T : X → Y be a compact operator, and let L : D(L) → Z be a closed and densely defined linear operator. Then the generalized singular value expansion (GSVE) is an expansion that expresses T and L in terms of a common orthonormal basis. Under certain hypotheses on discretization, the GSVE of an approximate operator pair (Tj, Lj), where Tj : XjYj and Lj : XjZj, converges to the GSVE of (T, L). Error estimates establish a rate of convergence that is consistent with numerical experiments in the case of discretization using piecewise linear finite elements. Further numerical testing suggests that a higher rate of convergence is attained by using higher order elements. However, the theory does not cover this case.

Indexing (document details)
Advisor: Gockenbach, Mark S.
Commitee: Masoud, Hassan, Ong, Benjamin W., Sun, Jiguang
School: Michigan Technological University
Department: Mathematical Sciences
School Location: United States -- Michigan
Source: DAI-B 80/09(E), Dissertation Abstracts International
Subjects: Applied Mathematics, Mathematics
Keywords: Generalized singular value expansion
Publication Number: 13863536
ISBN: 978-1-392-17368-8
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