Improving the Accuracy of Computed Eigenvalues and Eigenvectors

This paper describes and analyzes several variants of a computational method for improving the numerical accuracy of, and for obtaining numerical bounds on, matrix eigenvalues and eigenvectors. The method, which is essentially a numerically stable implementation of Newton’s method, may be used to “fine tune” the results obtained from standard subroutines such as those in EISPACK Lecture Notes in Computer Science 6, 51, Springer-Verlag, Berlin, 1976, 1977. Extended precision arithmetic is required in the computation of certain residuals.