Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
Inverse iteration is widely used to compute the eigenvectors of a matrix once accurate eigenvalues are known. We discuss various issues involved in any implementation of inverse iteration for real, symmetric matrices. Current implementations resort to reorthogonalization when eigenvalues agree to more than three digits relative to the norm. Such reorthogonalization can have unexpected consequences. Indeed, as we show in this paper, the implementations in EISPACK and LAPACK may fail. We illustrate with both theoretical and empirical failures.
Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
A. Gupta, R. Gross, et al.
SPIE Advances in Semiconductors and Superconductors 1990
David W. Jacobs, Daphna Weinshall, et al.
IEEE Transactions on Pattern Analysis and Machine Intelligence
Leo Liberti, James Ostrowski
Journal of Global Optimization