A continuation method for a weakly elliptic two-parameter eigenvalue problem

IMA Journal of Numerical Analysis

Volumn 21, Issue 1, 2001, Pages 199-216

  Plestenjak, Bor ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Continuation method; Homotopy bifurcation; Two parameter eigenvalue problem; Weakly elliptic

Indexed keywords

CONTINUATION METHOD; EIGENVALUE PROBLEM; HOMOTOPIES; NONSYMMETRIC; TWO PARAMETER; TWO-PARAMETER EIGENVALUE PROBLEM; WEAKLY ELLIPTIC;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0035529767     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/21.1.199     Document Type: Article

References (20)

1. ALLGOWER, E. L. & GEORG, K. 1990 Numerical Continuation Methods. Berlin: Springer.
2. ATKINSON, F. V. 1968 Multiparameter spectral theory. Bull. Am. Math. Soc. 74, 1-27..
3. ATKINSON, F. V. 1972 Multiparameter Eigenvalue Problems. New York: Academic.
4. BLUM, E. K. & CHANG, A. F. 1978 A numerical method for the solution of the double eigenvalue problem. J. Inst. Math. Appl. 22, 29-41.
5. BOHTE, Z. 1982 Numerical Solution of Some Two-parameter Eigenvalue Problems, Anton Kuhelj memorial volume, Ljubljana: Slov. Acad. Sci. Art., pp 17-28.
6. BROWNE, P. J. & SLEEMAN, B. D. 1982 A numerical technique for multiparameter eigenvalue problems. IMA J. Numer. Anal. 2, 451-457.
7. DONGARA, J. J. & SIDANI, M. 1992 A parallel algorithm for the nonsymmetric eigenvalue problem. Numerical Analysis 1991 (Dundee 1991) (Pitman Research Notes in Mathematics 260). (D. F. Griffits & G. A. Watson eds). Harlow: Longman Scientific and Technical, pp 85-102.
8. FAIERMAN, M. 1991 Two-parameter eigenvalue problems in ordinary differential equations. Pitman Research Notes in Mathematics 205. Harlow: Longman Scientific and Technical.
9. JI, X. 1992 A two-dimensional bisection method for solving two-parameter eigenvalue problems. SIAM J. Matrix Anal. Appl. 13, 1085-1093.
10. KOŠIR, T. 1994 Finite dimensional multiparameter spectral theory: the nonderogatory case. Lin. Alg. Appl. 212/213, 45-70.
11. KOŠIR, T. 1996 Kronecker bases for linear matrix equations, with application to two-parameter eigenvalue problems. Lin. Alg. Appl. 249, 259-288.
12. LI, T. Y., ZENG, Z., & CONG, L. 1992 Solving eigenvalue problems of real nonsymmetric matrices with real homotopies. SIAM J. Numer. Anal. 29, 229-248.
13. LI, T. Y. & WANG, X. 1993 Solving real polynomial systems with real homotopies. Math. Comput. 60, 669-680.
14. LI, T. Y. & WANG, X. 1994 Higher order turning points. Appl. Math. Comput. 64, 155-166.
15. MÜLLER, R. E. 1982 Numerical solution of multiparameter eigenvalue problems. Z. Angew. Math. Mech. 62, 681-686.
16. PLESTENJAK, B. 1998 A numerical algorithm for computing a basis for the root subspace at a nonderogatory eigenvalue of a multiparameter system. Lin. Alg. Appl. 285, 257-276.
17. PLESTENJAK, B. Continuation method for a right definite two-parametereigenvalue problem. SIAM J. Matrix Anal. Appl. To appear.
18. SHIMASAKI, M. 1995 Homotopy algorithm for two-parameter eigenvalue problems (Japanese). Trans. Japan SIAM 5, 121-129.
19. STEWART, G. W. 1985 A parallel implementation of the QR-algorithm. Parallel Comput. 5, 187-196.
20. VOLKMER, H. 1988 Multiparameter problems and expansion theorems. Lecture Notes in Mathematics 1356. New York: Springer.