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Fasta Lgorithm of Pseudo-Cholesky Factorization and the Backward Error Analysis for Eigenvalue Problems

Author: NiuQiHua
Tutor: LiuXinGuo
School: Ocean University of China
Course: Computational Mathematics
Keywords: Error Analysis Fast Algorithm Uniform rotation transformation Unified Householder transformation Backward error eigenvalue problem Matrix polynomial
CLC: O241.6
Type: Master's thesis
Year: 2005
Downloads: 104
Quote: 0
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Abstract


This paper consists of introduction, two chapters of the text content , as well as an appendices . Preface summarizes some important relevant developments , but also outlines the body part content. Text has two chapters . In the first chapter, first give some necessary preliminaries , and then gives a uniform rotation transformation and some basic properties of Householder transformations . Next, the application provides a fast algorithm for uniform rotation transformation . Algorithm is the core of the transformation is applied in a uniform 2-by- n matrix . Uniform rotation transformation satisfy Q ~ H (?) Q = S and the elimination of the first column of the matrix element of the second . By error analysis and numerical experiments can be seen with the direct application of a uniform rotation transformation compared to fast algorithm has the following two advantages: 1 , reduce the number of multiplications by about half , which can improve processing speed ; 2 , to avoid the application generates the diagonal matrix elements of the diagonal rapid increases and decreases in order to maintain good stability. The second chapter studies the real characteristics of the matrix on the complex approximation normwise backward error . Disturbance in the complex case , this issue has been resolved Higham et al . In this paper, the real disturbance situations . The results show that in general , the two cases is not very different , but in some cases , the two can vary greatly. As a promotion, we also discussed the problem of the matrix corresponding polynomials . One result of this paper is partially solved DJ Higham and NJ Higham 1999 , proposed a problem to be solved .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Linear algebra method of calculating
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