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BTTB Preconditioner for BTTB Least Squares Problems

Author: ZhangDeCai
Tutor: LinFuRong
School: Shantou University
Course: Applied Mathematics
Keywords: Least squares problem Preconditioned conjugate gradient method BTTB matrix Generating function Convergence rate
CLC: O151.21
Type: Master's thesis
Year: 2008
Downloads: 51
Quote: 0
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Abstract


In our many areas of science and engineering will be involved in the least squares problem , min ‖ b-Tx ‖ 2 . This paper considers the matrix T is an order by a relatively large number of Teplitz matrix or matrices BTTB case of a rectangular matrix , these problems in the image restoration , timing analysis has important application of this thesis consider using preconditioned conjugate gradient method to solve this least squares problem , and use Teplitz matrix and the BTTB matrix as a pretreatment factor in this calculation process of the main application of the one-dimensional and two-dimensional fast Fourier transform and inverse transform their paper is an in-depth understanding of least squares problems at home and abroad on the basis of focus based on polynomial approximation BTTB preconditioning matrix to solve the least squares problem . article is divided into two chapters, the main contents are as follows : The first chapter describes the research background and a summary of some of the research results obtained predecessors . associated with this article we introduce some of the basics, including Teplitz matrix , BTTB matrices and their generating function definitions , but also gives some of the symbols associated with this article , the basic concepts and theorems . Finally BTTB least squares problem preconditioned conjugate background gradient method second chapter to discuss in detail Teplitz least squares problem and BTTB least squares problem preconditioned conjugate gradient method. focused Teplitz preconditioning matrix and the BTTB preconditioning matrix structure , and their nature , we prove that they are valid preprocessing matrix constructed numerical examples show that the pretreatment of the matrix used in the cycle than the usual pre- factor is more effective. Finally, a summary of the article as well as prospects for the future .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Theory of algebraic equations,linear algebra > Linear Algebra > Matrix theory
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