The Orthogonal Rayleigh Quotient Iteration (ORQI) method

Linear Algebra and Its Applications

Volumn 358, Issue 1-3, 2003, Pages 23-43

  Dax, Achiya ^a  

^a Hydrological Service of Israel   (Israel)

Author keywords

Complete eigensystem; Eigenvalues; Eigenvectors; Rayleigh quotient iteration; Real symmetric band matrices; Reorthogonalization; Selective orthogonalization

Indexed keywords

EID: 84867949361     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0024-3795(01)00330-5     Document Type: Conference Paper

References (26)

1. S. Batterson, and J. Smillie The dynamics of Rayleigh quotient iteration SIAM J. Numer. Anal. 26 1989 624 636
2. C. Beattie, and D.W. Fox Localization criteria and containment for Rayleigh quotient iteration SIAM Matrix Anal. Appl. 10 1989 80 93
3. S. Chandrasekaran, and I.C.F. Ipsen Backward errors for eigenvalue and singular value decompositions Numer. Math. 68 1994 215 223
4. A. Dax A modified Gram-Schmidt algorithm with iterative orthogonalization and column pivoting Linear Algebra Appl. 310 2000 25 42
5. J.W. Demmel Applied Numerical Linear Algebra 1997 SIAM Philadelphia
6. 2) algorithm for the symmetric tridiagonal eigenvalue/eigenvector problem, Report No. UCB//CSD-97-971, October 1997, Computer Science Division, University of California, Berkeley, CA 94720
7. I.S. Dhillon and B.N. Parlett, Orthogonal eigenvectors and relative gaps, Technical Report, February 2000; SIAM J. Matrix anal. Appl. (submitted)
8. K.V. Fernando On computing an eigenvector of a tridiagonal matrix. Part I: Basic results SIAM J. Matrix Anal. Appl. 18 1997 1013 1034
9. M. Gu, and S.C. Eisenstat A divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem SIAM J. Matrix Anal. Appl. 16 1995 172 191
10. I.C.F. Ipsen Computing an eigenvector with inverse iteration SIAM Review 30 1997 254 291
11. I.C.F. Ipsen, and E.R. Jessup Solving the symmetric tridiagonal eigenvalue problem on the hypercube SIAM J. Sci. Statist. Comput. 11 1990 203 229
12. E.R. Jessup, and I.C.F. Ipsen Improving the accuracy of inverse iteration SIAM J. Sci. Statist. Comput. 13 1992 550 572
13. T.Y. Li, H. Zhang, and X.H. Sun Parallel homotopy algorithm for the symmetric tridiagonal eigenvalue problem SIAM J. Sci. Statist. Comput. 12 1991 469 487
14. R.S. Martin, and J.H. Wilkinson Solution of symmetric and unsymmetric band equations and the calculation of eigenvectors of band matrices Numer. Math. 9 1967 279 301
15. A.M. Ostrowski On the convergence of the Rayleigh quotient iteration for the computation of characteristic roots and vectors, I Arch. Rational Mech. Anal. 1 1958 233 241
16. A.M. Ostrowski On the convergence of the Rayleigh Quotient Iteration for the computation of characteristic roots and vectors, II Arch. Rational Mech. Anal. 2 1959 423 428
17. R.D. Pantazis, D.B. Szyld, Regions of convergence of the Rayleigh Quotient Iteration method, Report 92-101, Department of Mathematics, Temple University, 1993
18. B.N. Parlett The Rayleigh quotient iteration and some generalizations for nonnormal matrices Math. Comp. 28 1974 679 693
19. B.N. Parlett The Symmetric Eigenvalue Problem 1980 Prentice-Hall Englewood Cliffs, NJ
20. B.N. Parlett Invariant subspaces for tightly clustered eigenvalues of tridiagonals BIT 36 1996 542 562
21. B.N. Parlett, and I.S. Dhillon Fernando's solution to Wilkinson's problem: An application of double factorization Linear Algebra Appl. 267 1997 247 279
22. B.N. Parlett, and I.S. Dhillon Relatively robust representations of symmetric tridiagonals Linear Algebra Appl. 309 2000 121 151
23. B.N. Parlett, and J. Le Forward instability of tridiagonal QR SIAM J. Matrix Anal. Appl. 14 1993 279 316
24. B.N. Parlett, and O.A. Marques An implementation of the dqds algorithm (positive case) Linear Algebra Appl. 309 2000 217 259
25. D.B. Szyld Criteria for combining inverse and Rayleigh Quotient Iteration SIAM J. Numer. Anal. 25 1988 1369 1375
26. J.H. Wilkinson The Algebraic Eigenvalue Problem 1965 Oxford University Press Oxford