Strong rank revealing Cholesky factorization

Electronic Transactions on Numerical Analysis

Volumn 17, Issue , 2004, Pages 76-92

  Gu, M ^b   Miranian, L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b NONE

Author keywords

Cholesky decomposition; LU decomposition; Numerical rank; QR decomposition; Rank revealing; Singular values; Strong rank revealing QR factorization

Indexed keywords

EID: 3042538274     PISSN: 10689613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. A. Björck, Numerical methods for least squares problems, SIAM, Philadelphia, PA, USA, 1996.
2. A. Björck, A direct method for the solution of sparse linear least squares problems, in Large scale matrix problems, A. Björck, R. J. Plemmons, H. Schneider, eds., North-Holland, 1981.
3. P.A. Businger, G.H. Golub, Linear least squares solutions by Householder transformations, Numer. Math., 7 (1965), pp. 269-276.
4. T.F. Chan, On the existence and computation of LU factorizations with small pivots, Math. Comp., 42 (1984), pp. 535-547.
5. T.C. Chan, An efficient modular algorithm for coupled nonlinear systems, Research Report YALEU/DCS/RR-328, Sept. 1984.
6. S. Chandrasekaran, I. Ipsen, On rank revealing QR factorizations, SIAM J. Matrix Anal. Appl., 15 (1994), pp. 592-622.
7. J.W. Demmel, Applied Numerical Linear Algebra, SIAM, Philadelphia, PA, 1997.
8. R. Fletcher, Expected conditioning, IMA J. Numer. Anal., 5 (1985), pp. 247-273.
9. G.H. Golub, Numerical methods for solving linear least squares problems, Numer. Math., 7 (1965), pp. 206-216.
10. G.H. Golub, C.F. Van Loan, Matrix Computations, second ed., Johns Hopkins University Press, Baltimore, MD, USA, 1989.
11. M. Gu, S.C. Eisenstat, An efficient algorithm for computing a strong rank revealing QR factorization, SIAM J. Sci. Comput., 17 (1996), pp. 848-869.
12. W. W. Hager, Condition estimates, SIAM J. Sci. Statist. Comput., 5 (1984), pp. 311-317.
13. N.J. Higham, Analysis of the Cholesky decomposition of a semi-definite matrix, in M.G. Cox and S.J. Hammarling, eds., Reliable Numerical Computation, Oxford University Press, 1990, pp. 161-185.
14. N.J. Higham, Accuracy and stability of numerical algorithms, SIAM, January 1996.
15. Y.P. Hong, C.T. Pan, Rank revealing QR factorizations and the singular value decompositions, Math. Comp., 58 (1992), pp. 213-232.
16. R.A. Horn, C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
17. P. Hough, S. Vavasis, Complete orthogonal decomposition for weighted least squares, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 369-392.
18. T.-S. Hwang, W.-W. Lin, E.K. Yang, Rank revealing LU factorizations, Linear Algebra Appl., 175 (1992), pp. 115-141.
19. T.-S. Hwang, W.-W. Lin, D. Pierce, Improved bound for rank revealing LU factorizations, Linear Algebra Appl., 261 (1997), pp. 173-186.
20. W. Kahan, Numerical linear algebra, Canad. Math. Bull., 9 (1966), pp. 757-801.
21. C.D. Meyer, D. Pierce, Steps towards an iterative rank revealing method, Boeing Information and Support Services, ISSTECH-95-013, November 30, 1995.
22. C.-T. Pan, P.T. Tang, Bounds on singular values revealed by QR factorization, BIT, 39(4) (1999), pp. 740-756.
23. C.-T. Pan, On the existence and computation of rank revealing LU factorizations, Linear Algebra Appl., 316 (2000), pp. 199-222.
24. G. Peters, J.H. Wilkinson, The least-squares problem and pseudo-inverses, Comput. J., 13 (1970), pp. 309-316.
25. D. Pierce, J.G. Lewis, Sparse multi-frontal rank revealing QR factorization, SIAM J. Matrix Anal. Appl., 18 (1997), pp. 159-180.
26. G.W. Stewart, Updating a rank revealing ULV decomposition, SIAM J. Matrix Anal. Appl., 14 (1993), pp. 494-499.