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Methods for the numerical solution of the eigenvalue problem for real symetric matrices

University of British Columbia

The purpose of this thesis is to give a survey of the methods currently used to solve the numerical eigenvalue problem for real symmetric matrices. On the basis of the advantages and disadvantages inherent in the various methods, it is concluded that Householder's method is the best. Since the methods of Givens, Lanczos, and Householder use the Sturm sequence bisection algorithm as the final stage, a complete theoretical discussion of this process is included. Error bounds from a floating point error analysis (due to Ortega), for the Householder reduction are given. In addition, there is a complete error analysis for the bisection process.

Text

2011-11-21

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http://hdl.handle.net/2429/39176

Mathematics

University of British Columbia

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