The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices

摘要

The Rayleight Quotient Iteration (RQI) was developed for real symmetric matrices. Its rapid local convergence is due to the stationarity of the R.Q. at an eigenvector. Its excellent global properties are due to the monotonic decrease in the norms of the residuals. These facts are established for normal matrices. Both properties fail for nonnormal matrices and no generalization of the iteration has recaptured both of them. Methods are examined which employ either one or the other of them. (Author)