A Stable Divide and Conquer Algorithm for the Unitary Eigenproblem

Authors:
Ming Gu;Robert Guzzo;Xue-bin Chi;Xing-Qin Cao
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Matrix Analysis and Applications
Year:
2003

Citing 0
Cited 6

A unitary Hessenberg QR-based algorithm via semiseparable matrices

Journal of Computational and Applied Mathematics
Szegő-Lobatto quadrature rules

Journal of Computational and Applied Mathematics
Eigenvalue computation for unitary rank structured matrices

Journal of Computational and Applied Mathematics
Trigonometric orthogonal systems and quadrature formulae

Computers & Mathematics with Applications
Orthogonal Laurent polynomials on the unit circle and snake-shaped matrix factorizations

Journal of Approximation Theory
A unitary Hessenberg QR-based algorithm via semiseparable matrices

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a divide and conquer algorithm for computing the eigendecomposition of a unitary upper Hessenberg matrix H. Previous divide and conquer approaches suffer a potential loss of orthogonality among the computed eigenvectors of H. Using a backward stable method based on previous work by Gu and Eisenstat in the rank-one modification of the symmetric eigenproblem, our algorithm provides a backward stable method for computing the eigenvectors. The method also compares well against the efficiency of other available methods.