Candidate: Archara Chaiyakarn

Degree of: Doctor of Philosophy

Department: Mathematics

Title: Structure Preserving Algorithms for Computing the Symplectic Singular Value Decomposition

Committee: Dr. Niloufer Mackey, Chair
Dr. Dennis D. Pence
Dr. Clifton E. Ealy Jr.
Dr. Hongguo Xu

Date: Tuesday, November 30, 2004 3:00 p.m. – 5:00 p.m.
6625 Everett Tower, Alavi Commons

Abstract: In this Theses we develop two types of structure preserving Jacobi algorithms for computing the symplectic singular value decomposition of real symplectic matrices and complex symplectic matrices. Unlike general purpose algorithms, these algorithms produce symplectic structure in all factors of the singular value decomposition. Our first algorithm uses the relation between the singular value decomposition and the polar decomposition to reduce the problem of finding the symplectic singular value decomposition to that of calculating the structured spectral decomposition of a doubly structured matrix. A Jacobi-like method is developed to compute this doubly structured spectral decomposition.
The second algorithm is a one-sided Jacobi method that directly computes the structured singular value decomposition of real or complex symyplectic matrices.
Numerical experiments show that our algorithms converge quadratically. Furthermore, the number of sweeps needed for convergence is favorable when compared to Jacobi-like algorithms for other structured matrices.

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