Accurate computation of singular values in terms of shifted integrable schemes

Japan Journal of Industrial and Applied Mathematics

Volumn 23, Issue 3, 2006, Pages 239-259

  Iwasaki, Masashi ^a   Nakamura, Yoshimasa ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

Discrete Lotka Volterra system; Shift of origin; Singular value

Indexed keywords

EID: 33846029527     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167593     Document Type: Article

References (16)

1. Z. Bai, C. Bischof, L. S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Geenhaum, S. Hammarling, A. Mckenney, D. Sorensen and E. Anderson, Lapack Users' Guide (third edition). SIAM, Philadelphia, 2000, http://www.netlib.org/ lapack/.
2. J. Demmel, Accurate Singular Values of Bidiagonal Matrices. SIAM, Philadelphia, 1997.
3. J. Demmel and W. Kahan, Accurate singular values of bidiagonal matrices. SIAM Journal on Scientific Statistical Computing, 11 (1990), 873-912.
4. K.V. Fernando and B.N. Parlett, Accurate singular values and differential qd algorithms. Numerische Mathematik, 67 (1994), 191-229.
5. G.H. Golub and C. Reinsch, Singular value decomposition and least squares solutions. Numerische Mathematik, 14 (1970), 403-420.
6. G.H. Golub and C.F. Van Loan, Matrix Computations (third edition). John Hopkins University Press, Baltimore, 1996.
7. A. Heck, Introduction to Maple (third edition). Springer-Verlag, New York, 2003.
8. R. Hirota, Conserved quantities of a "random-time Toda equation." Journal of the Physical Society of Japan, 66 (1997), 283-284.
9. M. Iwasaki and Y. Nakamura, On a convergence of solution of the discrete Lotka-Volterra system. Inverse Problems, 18 (2002), 1569-1578.
10. M. Iwasaki and Y. Nakamura, An application of the discrete Lotka-Volterra system with variable step-size to singular value computation. Inverse Problems, 20 (2004), 553-563.
11. C.R. Johnson, A Gersgorin-type lower bound for the smallest singular value. Linear Algebra and its Applications, 112 (1989), 1-7.
12. H. Rutishauser, Lectures on Numerical Mathematics. Birkhäuser, Boston, 1990.
13. V. Spiridonov and A. Zhedanov, Discrete-time Volterra chain and classical orthogonal polynomial. Journal of Physics A: Mathematical and General, 30 (1997), 8727-8737.
14. S. Tsujimoto, Y. Nakamura and M. Iwasaki, The discrete Lotka-Volterra system computes singular values. Inverse Problems, 17 (2001), 53-58.
15. R.C. Whaley and J.J. Dongarra, Automatically tuned linear algebra software. Technical Report UT-CS-97-366, University of Tennessee, 1997, http://math-atlas.sourceforge.net/.
16. J.H. Wilkinson, The Algebraic Eigenvalue Problem. Clarendon Press, Oxford, 1965.