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Backward Error Analysis for Structured Unitary Matrix Eigenvalue Problems

Author: SiYuZuo
Tutor: LiuXinGuo
School: Ocean University of China
Course: Computational Mathematics
Keywords: Structured backward error Structural eigenvalue problem Structural unitary matrix
CLC: O241.6
Type: Master's thesis
Year: 2005
Downloads: 46
Quote: 2
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Abstract


Structured eigenvalue problems is an active area of ??research in numerical algebra community in the last decade , the problem itself is very rich in engineering and scientific background . Structured eigenvalue problems , computational mathematics major problem is the development of the algorithm for preserving structure ( Structure -preserving algorithm) , structured backward error can be used to test the stability of numerical algorithms strong . This article discusses the seven types of structure unitary matrix eigenvalue problem backward error . Backward error analysis of the seven types of dual structure matrix eigenvalue problem Tisseur 2003 paper [8 ] pending issues . One of the six types of problems , given expression, or more precisely on the backward error norm structure , the lower bound estimate . These estimator are relatively easy to calculate . - Of the remaining class of problems that its essence is a single structure matrix eigenvalue problem may have been the result to solve . The results can be seen as a positive answer to the problem mentioned Tisseur . This article is also part of the unitary matrix eigenvalues ??structural and non- structural norm backward error compared . More obvious differences between the two numerical examples , which illustrate the double structure of the unitary matrix eigenvalue problem of backward error . The text consists of five parts . The first part , we review the research progress of the backward error structure eigenvalue problem . A brief overview of the backward error analysis of the development and the advantages and disadvantages of the two main types of methods , as well as the structure of the eigenvalue problem of the actual application background and research progress , and further that the meaning and purpose of this study . The second part is divided into seven parts , respectively, of the seven types of structured unitary matrix eigenvalue problem backward error analysis . First six types of problems , we have given expression, or more precisely on the backward error norm structure , the lower bound estimate , while the rest of the class structure of the unitary matrix situation , its essence is a single structure matrix characteristics

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