Quotient-difference type generalizations of the power method and their analysis

摘要

The recursion relations that were proposed by Ford and Sidi (1988) for implementing vector extrapolation methods are used for devising generalizations of the power method for linear operators. These generalizations are shown to produce approximations to largest eigenvalues of a linear operator under certain conditions. They are similar in form to the quotient-difference algorithm and share similar convergence properties with the latter. These convergence properties resemble also those obtained for the basic LR and QR algorithms. Finally, it is shown that the convergence rate produced by one of these generalizations is twice as fast for normal operators as it is for nonnormal operators.