Algorithm 776: SRRIT: A Fortran Subroutine to Calculate the Dominant Invariant Subspace of a Nonsymmetric Matrix

ACM Transactions on Mathematical Software

Volumn 23, Issue 4, 1997, Pages 494-513

  Bai, Z ^a   Stewart, G W ^b  

^a UNIVERSITY OF KENTUCKY   (United States)

^b Institute of Advanced Computer Science   (United States)

Author keywords

D.3.2 Programming Languages : Language Classifications Fortran; F.2.1 Analysis of Algorithms and Problem Complexity : Numerical Algorithms and Problems computations on matrices; G.1.3 Numerical Analysis : Numerical Linear Algebra eigenvalues

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; FORTRAN (PROGRAMMING LANGUAGE); ITERATIVE METHODS; MATRIX ALGEBRA; PROBLEM SOLVING;

DOMINANT INVARIANT SUBSPACES; SOFTWARE PACKAGE SRRIT;

SUBROUTINES;

EID: 0031346306     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/279232.279234     Document Type: Article

References (18)

1. ANDERSON, E., BAI, Z., BISCHOF, C. H., DEMMEL, J., DONGARRA, J. J., DU CROZ, J., GREENBAUM, A., HAMMARLING, S., MCKENNEY, A., OSTROUCHOV, S., AND SORENSEN, D. C. 1995. LAPACK User's Guide. 2nd ed. Society for Industrial and Applied Mathematics, Philadelphia, PA.
2. BAI, Z. AND DEMMEL, J. 1993. On swapping diagonal blocks in real Schur form. Lin. Alg. Appl. 186, 73-95.
3. BAUER, F. L. 1957. Das verfahren der treppeniteration und verwandte verfahren zur lösung algebraischer eigenwertprobleme. Z. Angew. Math. Phys. 8, 214-235.
4. CLINT, M. AND JENNINGS, A. 1970. The evaluation of eigenvalues and eigenvectors of a real symmetric matrix by simultaneous iteration. Comput. J. 13, 68-80.
5. DUFF, I. S. AND SCOTT, J. A. 1993. Computing selected eigenvalues of sparse unsymmetric matrices using subspace iteration. ACM Trans. Math. Softw. 19, 2 (June), 137-159.
6. FELLER, W. 1961. An Introduction to Probability Theory and Its Applications. John Wiley & Sons, Inc., New York, NY.
7. JENNINGS, A. AND STEWART, W. J. 1971. A simultaneous iteration method for the unsymmetric eigenvalue problem. J. Inst. Math. Appl. 8, 111-121.
8. RUTISHAUSER, H. 1969. Computational aspects of F. L. Bauer's simultaneous iteration method. Numer. Math. 13, 4-13.
9. RUTISHAUSER, H. 1971. Simultaneous iteration method for symmetric matrices. Numer. Math. 16, 205-223.
10. SAAD, Y. 1984. Chebyshev acceleration techniques for solving nonsymmetric eigenvalue problems. Math. Comput. 42, 71-90.
11. SMITH, B. T., BOYLE, J. M., GARBOW, B. S., IKEBE, Y., KLEMA, V. C., AND MOLER, C. B. 1974. Matrix Eigensystem Routines: EISPACK Guide. Springer Lecture Notes in Computer Science, vol. 6. Springer-Verlag, Berlin, Germany.
12. STEWART, G. W. 1969. Accelerating the orthogonal iteration for the eigenvalues of a Hermitian matrix. Numer. Math. 13, 362-376.
13. STEWART, G. W. 1973. Introduction to Matrix Computations. Academic Press, Inc., Orlando, FL.
14. STEWART, G. W. 1976a. Simultaneous iteration for computing invariant subspaces of non-Hermitian matrices. Numer. Math. 25, 123-126.
15. STEWART, G. W. 1976b. ALGORITHM 506: HQR3 and EXCHNG: Fortran subroutines for calculating and ordering the eigenvalues of a real upper Hessenberg matrix. ACM Trans. Math. Softw. 2, 3 (Sept.), 275-280.
16. STEWART, G. W. 1978. SRRIT: A FORTRAN subroutine to calculate the dominant invariant subspace of a nonsymmetric marix. Tech. Rep. TR-154. Department of Computer Science, University of Maryland, College Park, MD.
17. STEWART, W. J. AND JENNINGS, A. 1981. ALGORITHM 570: LOPSI: A simultaneous iteration algorithm for real matrices. ACM Trans. Math. Softw. 7, 2 (June), 230-232.
18. WILKINSON, J. H. 1965. The Algebraic Eigenvalue Problem. Oxford University Press, Oxford, UK.