The orthogonal qd-algorithm

SIAM Journal on Scientific Computing

Volumn 18, Issue 4, 1997, Pages 1163-1186

  Von Matt, Urs ^a,b  

^a UNIVERSITY OF MARYLAND   (United States)

^b ETH ZURICH   (Switzerland)

Author keywords

Generalized Givens transformation; Laguerre's method; Orthogonal qd algorithm; Singular value decomposition

Indexed keywords

GENERALIZED GIVENS TRANSFORMATION; LAGUERRE METHOD; ORTHOGONAL QUADRATIC ALGORITHMS; SINGULAR VALUE DECOMPOSITION;

BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; VECTORS;

ALGORITHMS;

EID: 0031173555     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827594274887     Document Type: Article

References (29)

1. S. T. ALEXANDER, C.-T. PAN AND R. J. PLEMMONS, Analysis of a recursive least squares hyperbolic rotation algorithm for signal processing, Linear Algebra Appl., 98 (1988), pp. 3-40.
2. E. ANDERSON, Z. BAI, C. BISCHOF, J. DEMMEL, J. DONGARRA, J. DU CROZ, A. GREENBAUM, S. HAMMARLING, A. MCKENNEY, S. OSTROUCHOV, AND D. SORENSEN, LAPACK Users' Guide, SIAM, Philadelphia, PA, 1992.
3. A. W. BOJANCZYK, R. P. BRENT, P. VAN DOOREN, AND F. R. DE HOOG, A note on downdating the Cholesky factorization, SIAM J. Sci. Statist. Comput., 8 (1987), pp. 210-221.
4. P. DEIFT, J. DEMMEL, L.-C. LI, AND C. TOMEI, The bidiagonal singular value decomposition and Hamiltonian mechanics, SIAM J. Numer. Anal., 28 (1991), pp. 1463-1516.
5. J. DEMMEL AND W. KAHAN, Accurate singular values of bidiagonal matrices, SIAM J. Sci. Statist. Comput., 11 (1990), pp. 873-912.
6. J. J. DONGARRA, C. B. MOLER, J. R. BUNCH, AND G. W. STEWART, LINPACK Users' Guide, SIAM, Philadelphia, PA, 1979.
7. K. V. FERNANDO AND B. N. PARLETT, Accurate singular values and differential qd algorithms, Numer. Math., 67 (1994), pp. 191-229.
8. W. GANDER, L. MOLINARI, AND H. ŠVECOVÁ, Numerische Prozeduren aus Nachlass und Lehre von Prof. Heinz Rutishauser, International Series on Numerical Mathematics, Vol. 33, Birkhäuser, Basel, Switzerland, 1977.
9. G. H. GOLUB AND W. KAHAN, Calculating the singular values and pseudo-inverse of a matrix, SIAM J. Numer. Anal., 2 (1965), pp. 205-224.
10. G. H. GOLUB AND G. P. H. STYAN, Numerical computations for univariate linear models, J. Statist. Comput. Simulation, 2 (1973), pp. 253-274.
11. G. H. GOLUB AND C. F. VAN LOAN, Matrix Computations, 2nd ed., The Johns Hopkins University Press, Baltimore, MD, 1989.
12. E. HANSEN AND M. PATRICK, A family of root finding methods, Numer. Math., 27 (1977), pp. 257-269.
13. E. R. JESSUP AND I. C. F. IPSEN, Improving the accuracy of inverse iteration, SIAM J. Sci. Statist. Comput., 13 (1992), pp. 550-572.
14. W. KAHAN, Where does Laguerre's method come from? in Proc. Fourth Annual Princeton Conference on Information Sciences and Systems, Department of Electrical Engineering, Princeton University, Princeton, NJ, 1970, p. 143.
15. W. KAHAN, Notes on Laguerre's Iteration, University of California at Berkeley, Berkeley, CA, 1992, unpublished manuscript.
16. C. L. LAWSON, R. J. HANSON, D. R. KINCAID, AND F. T. KROGH, Basic linear algebra subprograms for Fortran usage, ACM Trans. Math. Software, 5 (1979), pp. 308-325.
17. T. Y. LI AND Z. ZENG, The Laguerre iteration in solving the symmetric tridiagonal eigenproblem, revisited, SIAM J. Sci. Comput., 15 (1994), pp. 1145-1173.
18. H. J. MAEHLY, Zur iterativen Auflösung algebraischer Gleichungen, Z. Angew. Math. Phys., 5 (1954), pp. 260-263.
19. R. MATHIAS AND G. W. STEWART, A block QR algorithm and the singular value decomposition, Linear Algebra Appl., 182 (1993), pp. 91-100.
20. M. MOONEN, P. VAN DOOREN, AND F. VANPOUCKE, On the QR algorithm and updating the SVD and the URV decomposition in parallel, Linear Algebra Appl., 188/189 (1993), pp. 549-568.
21. A. M. OSTROWSKI, Solution of Equations in Euclidean and Banach Spaces, Solution of Equations and Systems of Equations, 3rd ed., Academic Press, New York, 1973.
22. B. N. PARLETT, Laguerre's method applied to the matrix eigenvalue problem, Math. Comp., 18 (1964), pp. 464-485.
23. B. N. PARLETT, The Symmetric Eigenvalue Problem, Prentice-Hall, Englewood Cliffs, NJ, 1980.
24. H. RUTISHAUSER, Der Quotienten-Differenzen-Algorithmus, Z. Angew. Math. Phys., 5 (1954), pp. 233-251.
25. H. RUTISHAUSER, Lectures on Numerical Mathematics, Birkhäuser Boston, Cambridge, MA, 1990.
26. G. W. STEWART, An updating algorithm for subspace tracking, IEEE Trans. Signal Processing, 40 (1992), pp. 1535-1541.
27. G. W. STEWART, On the stability of sequential updates and downdates, IEEE Trans. Signal Processing, 43 (1995), pp. 2642-2648.
28. U. VON MATT, Large Constrained Quadratic Problems, Verlag der Fachvereine, Zürich, 1993.
29. J. H. WILKINSON, The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, U.K., 1965.