James Lee Hafner
Journal of Number Theory
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.
James Lee Hafner
Journal of Number Theory
Heng Cao, Haifeng Xi, et al.
WSC 2003
Lurng-Kuo Liu
Proceedings of SPIE - The International Society for Optical Engineering
Robert S. Nelson, Zoran L. Barbaric, et al.
Proceedings of SPIE 1989