Computing projections with LSQR

BIT Numerical Mathematics

Volumn 37, Issue 1, 1997, Pages 96-104

  Saunders, Michael A ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Conjugate gradient method; Golub Kahan process; Least squares; Regularization

Indexed keywords

EID: 0005462653     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02510175     Document Type: Article

References (13)

1. Å. Bj̈orck, Conjugate gradient methods for sparse least squares problems, unpublished notes, Stanford University, 1979.
2. Å. Björck, A bidiagonalization algorithm for solving ill-posed systems of linear equations, Report LITH-MAT-R-80-33, Dept. of Mathematics, Linköping University, Linköping, Sweden, 1980.
3. Å. Björck, T. Elfving, and Z. Strakoš, Stability of conjugate gradient and Lanczos methods for linear least squares problems, SIAM J. Matrix Anal. Appl., to appear.
4. J. E. Craig, The N-step iteration procedures, J. Math. and Phys., 34, 1 (1955), pp. 64-73.
5. D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra, Freeman, London, 1963.
6. G. H. Golub and W. Kahan, Calculating the singular values and pseudoinverse of a matrix, SIAM J. Numer. Anal., 2 (1965), pp. 205-224.
7. G. H. Golub and C. F. Van Loan, Matrix Computations, Second Edition, The Johns Hopkins University Press, Baltimore and London, 1989.
8. A. Greenbaum, Estimating the attainable accuracy of recursively computed residual methods, SIAM J. Matrix Anal. Appl., to appear.
9. M. R. Hestenes and E. Stiefel, Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Stds., B49 (1952), pp. 409-436.
10. C. C. Paige, Bidiagonalization of matrices and solution of linear equations, SIAM J. Numer. Anal., 11 (1974), pp. 197-209.
11. C. C. Paige and M. A. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software, 8(1) (1982), pp. 43-71.
12. C. C. Paige and M. A. Saunders, Algorithm 583. LSQR: Sparse linear equations and least squares problems, ACM Trans. Math. Software, 8(2) (1982), pp. 195-209.
13. M. A. Saunders, Solution of sparse rectangular systems using LSQR and CRAIG, BIT, 35 (1995), pp. 588-604.