Computing the Spectral Decomposition of Symmetric Matrices and the Singular Value Decomposition of Nonsymmetric Matrices with Guaranteed Accuracy

摘要

A new implementation of the Godunov-inverse iteration, that is, inverse iteration with guaranteed accuracy, is presented. A new implementation of the Cullum-Willoughby-Lanczos method, that is the Lanczos method, with guaranteed accuracy for computing the partial spectral decomposition of real symmetric matrices and the partial singular value decomposition of large sparse nonsymmetric matrices, is also presented. An inverse iteration with guaranteed accuracy is used for estimating the accuracy and, if necessary, for computing eigenvectors and singular vectors.