On extensions of the power method for normal operators
In a recent work by the author and \textit{J. Bridger} [J.Comput. Appl. Math. 22, 35-61 (1988; Zbl 0646.65030)] some old and some new extensions of the power method have been considered. It has been shown for some of these extensions that they enable one to estimate several dominant eigenvalues of an arbitrary square matrix. This paper continues this analysis for one of these extensions, namely, the minimal polynomial extrapolation (MPE) extension, as it is employed in estimating the dominant eigenvalues of a normal matrix. Section 1 gives a brief description of two versions of the MPE extension of the power method. Section 2 shows that the convergence rate of these methods for normal matrices is twice that for nonnormal matrices. Section 3 suggests deflation-type extensions of the power method for normal matrices and analyzes their convergence.
minimal polynomial extrapolation extension
scientific article; zbMATH DE number 4111900