An evaluation of singular value computation by the discrete lotka-volterra system

Proceedings of the 2005 International Conference on Parallel and Distributed Processing Techniques and Applications, PDPTA'05

Volumn 2, Issue , 2005, Pages 410-416

  Takata, Masami ^a   Kimura, Kinji ^b   Iwasaki, Masashi ^a   Nakamura, Yoshimasa ^a  

^a KYOTO UNIVERSITY   (Japan)

^b RIKKYO UNIVERSITY   (Japan)

Author keywords

Accuracy; Discrete lotka volterra system; LAPACK; LAPIS; Singular value

Indexed keywords

CONVERGENCE AND STABILITY; LOTKA-VOLTERRA; LOTKA-VOLTERRA SYSTEMS; NUMERICAL ACCURACY; SINGULAR VALUES;

DISTRIBUTED PARAMETER NETWORKS;

BIOLOGICAL SYSTEMS;

EID: 33847242875     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (16)

1. Demmel, J.: Applied Numerical Linear Algebra, SIAM, Philadelphia (1997).
2. Demmel, J., and Kahan, W.: Accurate singular values of bidiagonal matrics, SIAM J. Sci. Sta. Comput., Vol.67, pp. 191-229 (1994).
3. Dhillon, I. S., and Parlett, B. N.: Orthogonal eigenvectors and relative gaps, SIAM J. Matrix Anal. Appl., Vol.25, No.3, pp. 858-899 (2004).
4. Fernando, K. V., and Parlett, B. N.: Accurate singular values and differential qd algorithms, Numer. Math., Vol.67, pp. 191-229 (1994).
5. Francis, J. G. F.: The QR transformation a unitary analogue to the LR transformation-part 1, Computer J., Vol.4, pp. 265-271 (1961).
6. Golub, G., and Kahan, W.: Calculating the singular values and pseudo-inverse of a matrix, J. SIAM. Numer. Anal., Ser. B 2, pp. 205-224 (1965).
7. Golub, G., and Reinsch, C.: Singular value decomposition and least squares solutions, Numer. Math., Vol.14, pp. 403-420 (1970).
8. Henrici, P.: Applied and Computational Complex Analysis Volume I, Wiley-Interscience Publishing, New York (1988).
9. Iwasaki, M.: Studies of Singular Value Decomposition in Terms of Integrable Systems, Doctor Thesis, Kyoto University (2004).
10. Iwasaki, M., and Nakamura, Y.: On the convergence of a solution of the discrete LotkaVolterra system, Inverse Problems Vol.18, pp. 1569-1578 (2002).
11. Iwasaki, M., and Nakamura, Y.: Accurate computation of singular values in terms of the shifted integrable algorithm, (2005). (in preparation)
12. Johnson, C. R.: A Gersgorin-type lower bound for the smallest singular value, Lin. Alg. Appl., Vol.112, pp. 1-7 (1989).
13. LAPACK, http://www.netlib.org/lapackpp
14. NAG Numerical Libraries, http://www. nag. co.uk/
15. Parlett, B. N., and Marques, O. A.: An Implementation of the dqds Algorithm (Positive Case), Proc. of the International Workshop on Accurate Solution of Eigenvalue Problems (University Park, PA, 1998), Lin. Alg. Appl. 309, No. 1-3, pp. 217-259 (2000).
16. Rutishauser, H.: Der Quotienten-Differenzen-Algorithmus, Z. Angre. Math. Mech., Vol.5, pp. 233-251 (1954). (in Germany)