Date of Award
4-2005
Degree Name
Doctor of Philosophy
Department
Mathematics
Abstract
In this thesis we develop two types of structure preserving Jacobi algorithms for com puting 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 th a t of calculating the structured spectral decomposition of a doubly structured m atrix. A Jacobi-like m ethod is developed to compute this doubly structured spectral decomposition.
The second algorithm is a one-sided Jacobi m ethod th a t directly computes the structured singular value decomposition of real or complex symyplectic matrices.
Numerical experiments show th a t our algorithms converge quadratically. Furthermore, the number of sweeps needed for convergence is favorable when compared to Jacobi-like algorithms for other structured matrices.
Access Setting
Dissertation-Open Access
Recommended Citation
Chaiyakarn, Archara, "Structure Preserving Algorithms for Computing the Symplectic Singular Value Decom Position" (2005). Dissertations. 1022.
https://scholarworks.wmich.edu/dissertations/1022