Type of Document Master's Thesis Author Kimitei, Symon Kipyagwai Author's Email Address kimitei@hotmail.com URN etd-04182008-174330 Title Algorithms for Toeplitz Matrices with Applications to Image Deblurring Degree Master of Science Department Mathematics and Statistics Advisory Committee
Advisor Name Title Dr. Michael Stewart Committee Chair Dr. George Davis Committee Member Dr. Johannes Hattingh Committee Member Dr. Valerie Miller Committee Member Keywords
- Gohberg-Semencul formula
- Tikhonov Regularization
- Ill-posed problem
- Schur algorithm
- Toeplitz matrix
Date of Defense 2005-04-12 Availability unrestricted 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.
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