Trang H. Tran, Lam Nguyen, et al.
INFORMS 2022
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.
Trang H. Tran, Lam Nguyen, et al.
INFORMS 2022
Robert Manson Sawko, Malgorzata Zimon
SIAM/ASA JUQ
Heng Cao, Haifeng Xi, et al.
WSC 2003
Tong Zhang, G.H. Golub, et al.
Linear Algebra and Its Applications