CONVERGENCE AND STABILITY ANALYSES FOR SOME VECTOR EXTRAPOLATION METHODS IN THE PRESENCE OF DEFECTIVE ITERATION MATRICES

In two previous papers convergence and stability results for the following vector extrapolation methods were presented. Minimal Polynomial Extrapolation, Reduced Rank Extrapolation, Modified Minimal Polynomial Extrapolation, and Topological Epsilon Algorithm. The analyses were carried out for vector sequences that include those arising from iterative methods for linear systems of equations having diagonalizable iteration matrices. In this paper the analyses of the earlier papers are extended to vector sequences that include those arising from iterative methods for linear systems having defective iteration matrices. The results are illustrated with numerical examples. The analyses above naturally suggest some old and some new extensions of the well known power method, enabling one to obtain estimates for several dominant eigenvalues of a general matrix.