Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)


Homotopy-determinant algorithm for solving nonsymmetric eigenvalue problems

Authors: T. Y. Li and Zhong Gang Zeng
Journal: Math. Comp. 59 (1992), 483-502
MSC: Primary 65F15; Secondary 65F40, 65H17, 65H20
MathSciNet review: 1151113
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The eigenvalues of a matrix A are the zeros of its characteristic polynomial

$\displaystyle f(\lambda ) = \det [A - \lambda I].$

With Hyman's method of determinant evaluation, a new homotopy continuation method, homotopy-determinant method, is developed in this paper for finding all eigenvalues of a real upper Hessenberg matrix. In contrast to other homotopy continuation methods, the homotopy-determinant method calculates eigenvalues without computing their corresponding eigenvectors. Like all homotopy methods, our method solves the eigenvalue problem by following eigen-value paths of a real homotopy whose regularity is established to the extent necessary. The inevitable bifurcation and possible path jumping are handled by effective processes.

The numerical results of our algorithm, and a comparison with its counterpart, subroutine HQR in EISPACK, are presented for upper Hessenberg matrices of numerous dimensions, with randomly generated entries. Although the main advantage of our method lies in its natural parallelism, the numerical results show our algorithm to be strongly competitive also in serial mode.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65F15, 65F40, 65H17, 65H20

Retrieve articles in all journals with MSC: 65F15, 65F40, 65H17, 65H20

Additional Information

PII: S 0025-5718(1992)1151113-4
Article copyright: © Copyright 1992 American Mathematical Society