116
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Preconditioned conjugate gradient method for rank deficient least-squares problems

&
Pages 509-518 | Received 11 May 1998, Published online: 19 Mar 2007

References

  • Axelsson , O. and Lindskog , G. 1986 . On the rate of convergence of the preconditioned conjugate gradient method . Numer. Math. , 48 : 499 – 523 .
  • Bhimasankaram , P. , Sengupta , D. and Ramanathan , S. 1995 . Recursive inference in a general linear model . Sankhya, Ser. A , 57 : 227 – 255 .
  • Björck , Å and Yuan , J. Y. 1998 . Preconditioner for Least Squares Problems by LU Decomposition . ETNA , 8 : 26 – 35 .
  • Campbell S. L. Rank deficient least squares and the numerical solution of linear singular implicit systems of differential equations Linear Algebra and its role in Systems Theory 1985 51 63 Proc. AMS-IMS-SIAM Conf., Brunswick/Maine 1984, Contemp. Math., 47
  • Freund , R. 1987 . A note on two block SOR methods for sparse least-squares problems . LAA , 88/89 : 211 – 221 .
  • Ghavimi , A. R. and Laub , A. J. 1995 . An implicit deflation method for ill-conditioned Sylvester and Lyapunov equations . Int. J. Control , 61 : 1119 – 1141 .
  • Luo Z. Yuan J. Y. Silva B. P. B Notes on Direct Projection Method Technical Report Department of Mathematics, UFPR 1997
  • Markham , T. L. , Neumann , M. and Plemmons , R. J. 1985 . Convergence of a direct-iterative method for large-scale least squares problems . LAA , 69 : 155 – 167 .
  • Miller , V. A. and Neumann , M. 1987 . Successive Overrelaxation Methods for Solving the Rank Deficient Least Squares Problem . LAA , 88/89 : 533 – 557 .
  • Santos , C. H. , Silva , B. P. B. and Yuan , J. Y. 1998 . Block SOR methods for rank deficient least squares problems . JCAM , 100 : 1 – 9 .
  • Silva , B. P. B. 1997 . “ Master Dissertation ” . In Topics on Numerical Linear Algebra , Brazil : UFPR .
  • Silva B. P. B Yuan J. Y. Preconditioner for least squares problems by QR decomposition Technical Report Department of Mathematics, UFPR Brazil 1997

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.