Technical Report CS0529

TR#:CS0529
Class:CS
Title: On Extensions of the Power Method for Normal Operators
Authors: Avram Sidi
PDFCS0529.pdf
Abstract: In a recent work [1] 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, denoted in [1] as the MPE extension, as they are applied to nonnal matrices. We show that the convergence of these methods for nonnal matrices is twice that for nonnonnal 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 nonnal 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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