Generalized eigenvalue problems: Lanczos algorithm with a recursive partitioning method

Computers and Mathematics with Applications

Volumn 39, Issue 7-8, 2000, Pages 211-224

  Sundar, S ^a   Bhagavan, B K ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; NUMERICAL ANALYSIS; PROBLEM SOLVING; RECURSIVE FUNCTIONS; RESPONSE TIME (COMPUTER SYSTEMS); STIFFNESS MATRIX;

GENERALIZED EIGENVALUE PROBLEMS; KRYLOV SUBSPACE; LANCZOS ALGORITHM; RECURSIVE PARTITIONING ALGORITHM; STURM SEQUENCE BISECTION METHOD;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0034174062     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(00)00077-8     Document Type: Article

References (22)

1. A.S. Householder and F.L. Bauer, On certain methods for expanding the characteristic polynomial, Numer. Math, l (1), 29 (1959).
2. J.H. Wilkinson, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, (1965).
3. K.J. Bathe and E.L. Wilson, Large eigenvalue problems in dynamic analysis, ASCE J. Engng. Mech. Div. 98, 1471-1485 (1972).
4. K.J. Bathe, Finite Element Procedures in Engineering Analysis, Prentice-Hall of India Pvt. Ltd, (1990).
5. P.C. Chowdhury, The truncated Lanczos algorithm for partial solution of the symmetric eigenproblem, Comput. Structures 6, 439-446 (1976).
6. B.N. Parlett and D.S. Scott, The Lanczos algorithm with selective orthogonalization, Math. Comp., 217-238 (1979).
7. B.N. Parlett, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, (1980).
8. S. Pissanetzky, Sparse Matrix Technology, Academic Press, London, (1984).
9. B. Nour-Omid, B.N. Parlett, T. Ericsson and S. Jensen, How to implement the spectral transformation, Math. Comp. 48 (178), 663-673 (1987).
10. B. Nour-Omid, B.N. Parlett and R.L. Taylor, Lanczos versus subspace iteration for solution of eigenvalue problems, Int. Jr. Numer. Methods Engg. 19, 859-871 (1983).
11. J. Cullum, W. Kerner and R.A. Willoughby, A generalized nonsymmetric Lanczos procedure, Comp. Phys. Comm 53, 19-48 (1989).
12. C. Lanczos, An iteration method for the solution of the eigenvalue problem of linear differential and integral operators, J. Res. Nat. Bur. Standards 45, 255-282 (1950).
13. C.C. Paige, The computation of eigenvalues and eigenvectors of very large sparse matrices, Ph.D. Thesis, London University, (1971).
14. T. Ericsson and A. Ruhe, The spectral transformation Lanczos method, Math. Comp. 34, 1251-1268 (1980).
15. th Int. Conference on Computing Civil and Building Engineering, Berlin, Germany, July 12-15, 1995.
16. Y. Aoyama, K. Hirama and G. Yagawa, A parallel triangular decomposition algorithm on a workstation netwark with application to structural vibration analysis, Comp. Mechanics 19, 411-419 (1997).
17. S. Sundar, B.K. Bhagavan and A. Datta, Computing eigenvalues: Lanczos alogorithm with a new recursive partitioning method, Computers Math. Applic. (1998).
18. th Edition, McGraw-Hill, London, (1989).
19. W.W. Hager, Applied Numerical Linear Algebra, Prentice-Hall, (1988).
20. W. Barth, R.S. Martin and J.H. Wilkinson, Calculation of the eigenvalues of a symmetric tridiagonal matrix by the method of bisection, Numer. Math. 9, 386-393 (1967).
21. B.N. Datta, Numerical Linear Algebra and Applications, Brooks/Core Publishing, An International Thomson Publishing Company, (1995).
22. K.K. Gupta, Solution of eigenvalue problem by Sturm sequence method, Int. J. Numer. Meth. Eng. 49, 379-404 (1972).