On Computing Givens Rotations Reliably and Efficiently

ACM Transactions on Mathematical Software

Volumn 28, Issue 2, 2002, Pages 206-238

  Bindel, David ^a   Demmel, James ^a   Kahan, William ^a   Marques, Osni ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

G.4 Mathematical Software : Efficiency; reliability and robustness

Indexed keywords

EID: 0041413300     PISSN: 00983500     EISSN: None     Source Type: Journal    
DOI: 10.1145/567806.567809     Document Type: Article

References (19)

1. ANDERSON, E. 2000. Discontinuous plane rotations and the symmetric eigenvalue problem. Computer Science Dept. Tech. Rep. CS-00-454. Univ. Tennessee, Knoxville, Tenn. www.netlib.org/ lapack/lawns/lawn150.ps.
2. ANDERSON, E., BAI, Z., BISCHOF, C., DEMMEL, J., DONGARRA, J., DU CROZ, J., GREENBAUM, A., HAMMARLING, S., MCKENNEY, A., BLACKFORD, S., AND SORENSEN, D. 1999. LAPACK Users' Guide 3rd ed. SIAM, Philadelphia, Pa.
3. ANDERSON, E. AND FAHEY, M. 1997. Performance improvements to LAPACK for the Cray scientific library. Computer Science Dept. Tech. Rep. CS-97-359. Univ. Tennessee, Knoxville, Tenn. www.netlib.org/lapack/lawns/lawn126.ps.
4. ANSI/IEEE Std 754-1985, IEEE Standard for Binary Floating Point Arithmetic. ANSI/IEEE, New York.
5. BINDEL, D., DEMMEL, J., KAHAN, W., AND MARQUES, O. 2002. Software for reliable and efficient Givens rotations.www.cs.berkeley.edu/~demmel/Givens.
6. BLACKFORD, S., CORLISS, G., DEMMEL, J., DONGARRA, J., DUFF, I., HAMMARLING, S., HENRY, G., HEROUX, M., HU, C., KAHAN, W., KAUFMAN, L., KEARFOTT, B., KROGH, F., LI, X., MAANY, Z., PETITET, A., POZO, R., REMINGTON, K., WALSTER, W., WHALEY, C., WOLFF V. GUDENBERG, J., AND LUMSDAINE, A. 2001. Basic Linear Algebra Subprograms Technical (BLAST) Forum Standard. Intern. J. High Performance Comput. 15, 3-4 (also available at www.netlib.org/blas/blast-forum/).
7. DEMMEL, J. 1997. Applied Numerical Linear Algebra. SIAM, Philadelphia, Pa.
8. DEMMEL, J. AND LI, X. 1994. Faster numerical algorithms via exception handling. IEEE Trans. Comput. 43, 8, 983-992. LAPACK Working Note 59.
9. DONGARRA, J., BUNCH, J., MOLER, C., AND STEWART, G. W. 1979. LINPACK User's Guide. SIAM, Philadelphia, Pa.
10. GOLUB, G. AND VAN LOAN, C. 1996. Matrix Computations, 3rd ed. Johns Hopkins University Press, Baltimore, Md.
11. HULL, T., FAIRGRIEVE, T., AND TANG, P. T. P. 1994. Implementing complex elementary functions using exception handling. ACM Trans. Math. Softw. 20, 2 (June), 215-244.
12. HULL, T., FAIRGRIEVE, T., AND TANG, P. T. P. 1997. Implementing complex Arcsine and Arccosine using exception handling. ACM Trans. Math. Softw. 23, 3 (Sept), 299-335.
13. IEEE 754-2002. IEEE Standard for Binary Floating Point Arithmetic Revision. grouper.ieee.org/groups/754.
14. KATO, T. 1980. Perturbation Theory for Linear Operators, 2 ed. Springer-Verlag, Berlin, Germany.
15. KUNKEL, P. AND MEHRMANN, V. 1991. Smooth factorizations of matrix valued functions and their derivatives. Num. Math. 60, 115-132.
16. LAWSON, C., HANSON, R., KINCAID, D., AND KROGH, F. 1979. Basic linear algebra subprograms for Fortran usage. ACM Trans. Math. Softw. 5, 308-323.
17. SMITH, B. T., BOYLE, J. M., DONGARRA, J. J., GARBOW, B. S., IKEBE, Y., KLEMA, V. C., AND MOLER, C. B. 1976. Matrix Eigensystem Routines - EISPACK Guide. Lecture Notes in Computer Science, vol. 6. Springer-Verlag, Berlin, Germany.
18. STEWART, G. W. 1976. The economical storage of plane rotations. Numer. Math. 25, 2, 137-139.
19. WILKINSON, J. H. 1965. The Algebraic Eigenvalue Problem. Oxford University Press, Oxford, England.