Algorithm 853: An efficient algorithm for solving rank-deficient least squares problems

ACM Transactions on Mathematical Software

Volumn 32, Issue 1, 2006, Pages 157-165

  Foster, Leslie ^a   Kommu, Rajesh ^a,b  

^a SAN JOSE STATE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Least squares; QR factorization; Rank deficient

Indexed keywords

LEAST SQUARES; QR FACTORIZATION; RANK-DEFICIENT;

ALGORITHMS; CODES (SYMBOLS); LEAST SQUARES APPROXIMATIONS; MATRIX ALGEBRA; NUMERICAL METHODS;

PROBLEM SOLVING;

EID: 33745232326     PISSN: 00983500     EISSN: 00983500     Source Type: Journal    
DOI: 10.1145/1132973.1132981     Document Type: Article

References (11)

1. ANDEHSON, E., BAI, Z., BISCHOF, C., BLACKFORD, S., DEMMEL, J., DONGARRA, J., CROZ, J. D., GEEENBAUM, A., HAMMAELING, S., MCKENNEY, A., AND SORENSEN, D. 1999. LAPACK Users' Guide, 3rd ed. SLAM, Philadelphia.
2. BISCHOF, C. H. 1990. Incremental condition estimation. SIAM J. Matrix Anal. Appl. 11, 312-322.
3. BISCHOF, C. H. AND QUINTANA-ORTI, G. 1998. Algorithm 782: Codes for rank-revealing qr factorizations of dense matrices. ACM Trans. Math. Softw. 24, 254-257.
4. BUSINGER, P. AND GOLUB, G. H. 1965. Linear least squares solutions by Householder transformations. Numer. Math. 7, 269-276.
5. EISENSTAT, S. AND Gu, M. 1996. Efficient algorithms for computing a strong rank-revealing qr factorizations. SIAM J. Sci. Comput. 17, 848-869.
6. ENTING, I. G. 2002. Inverse Problems in Atmospheric Constituent Transport. Cambridge University Press, Cambridge.
7. FOSTER, L. V. 2003. Solving rank-deficient and ill-posed problems using UTV and QR factorizations. SIAMJ. Matrix Anal. Appl. 25, 582-600.
8. GOLUB, G. AND VANLOAN, C. F. 1996. Matrix Computations. John Hopkins, Baltimore, Md.
9. HANSEN, P. C. 1998. Rank-Deficient and Discrete Ill-Posed Problems. SIAM, Philadelphia.
10. QUINTANA-ORTI, G., SUN, X., AND BISCHOF, C. H. 1998. A BLAS-3 version of the QR factorization with column pivoting. SIAM J. Sci. Comput. 19, 1486-1494.
11. STEWART, G. W. 1998. Matrix Algorithms vol. 1: Basic Decompositions. SIAM, Philadelphia.