Abstract
In a recent work by Sidi and Bridger some old and some new extensions of the power method have been considered, and some of these extensions have been shown to produce estimates of several dominant eigenvalues of an arbitrary square matrix. In the present work we continue the analysis of two versions of one of these extensions, called the MPE extensions, as they are applied to normal matrices. We show that the convergence rate of these methods for normal matrices is twice that for nonnormal matrices. We also give precise asymptotic bounds on the errors of the estimates obtained for the eigenvalues. Further deflation-type extensions of the power method for normal matrices are suggested and analyzed for their convergence. All the results are stated and proved in the general setting of inner-product spaces.
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