Date of Award

4-21-2008

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics and Statistics

First Advisor

Dr. Michael Stewart - Chair

Second Advisor

Dr. Johannes Hattingh

Third Advisor

Dr. Valerie Miller

Fourth Advisor

Dr. George Davis

Abstract

In this thesis, we present the O(n(log n)^2) superfast linear least squares Schur algorithm (ssschur). The algorithm we will describe illustrates a fast way of solving linear equations or linear least squares problems with low displacement rank. This program is based on the O(n^2) Schur algorithm speeded up via FFT. The algorithm solves a ill-conditioned Toeplitz-like system using Tikhonov regularization. The regularized system is Toeplitz-like of displacement rank 4. We also show the effect of choice of the regularization parameter on the quality of the image reconstructed.

Included in

Mathematics Commons

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