Homotopy-determinant algorithm for solving nonsymmetric eigenvalue problems

Journal Article · Thu Oct 01 00:00:00 EDT 1992 · Mathematics of Computation; (United States)

DOI:https://doi.org/10.1090/S0025-5718-1992-1151113-4· OSTI ID:6701813

Li, T Y; Zeng, Zhonggang

The eigenvalues of a matix A are the zeros of its characteristic polynomial 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 eigenvalue 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. 18 refs., 4 figs., 1 tab.

• OSTI ID: 6701813
• Journal Information: Mathematics of Computation; (United States), Journal Name: Mathematics of Computation; (United States) Vol. 59:200; ISSN 0025-5718; ISSN MCMPAF
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
ALGORITHMS
COMPUTER CALCULATIONS
COMPUTERS
EIGENVALUES
EIGENVECTORS
FUNCTIONS
MATHEMATICAL LOGIC
MATHEMATICS
MATRICES
PARALLEL PROCESSING
POLYNOMIALS
PROGRAMMING