33
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Numerical solution of symmetric least-squares problems with an inversion-free Kovarik-type algorithm

&
Pages 271-286 | Received 26 Jan 2006, Accepted 24 Mar 2007, Published online: 02 Oct 2008

References

  • Björck , A. 1996 . Numerical Methods for Least Squares Problems , Philadelphia : SIAM .
  • Mohr , M. , Popa , C. and Rüde , U. 2004 . An iterative algorithm for approximate orthogonalisation of symmetric matrices . International Journal of Computer Mathematics , 81 ( 2 ) : 215 – 226 .
  • Kovarik , S. 1970 . Some iterative methods for improving orthogonality . SIAM Journal on Numerical Analysis , 7 ( 3 ) : 386 – 389 .
  • Hansen , P. C. 1998 . Rank-Deficient and Discrete Ill-posed Problems: Numerical Aspects of Linear Inversion , Philadelphia : SIAM .
  • Evans , D. J. and Popa , C. 2001 . Projections and preconditioning for inconsistent least-squares problems . International Journal of Computer Mathematics , 78 ( 4 ) : 599 – 616 .
  • Golub , G. H. and van Loan , C. F. 1996 . Matrix Computations , Baltimore : The John Hopkins University Press .
  • Mohr , M. , Popa , C. and Rüde , U. 2003 . “ Numerical solution of least-squares problems by a modified Kovarik algorithm. Technical Report ” . Friedrich-Alexander-Universität Erlangen-Nürnberg . 03–7, Lehrstuhl für Informatik 10 (Systemsimulation)
  • Boullion , L. T. and Odell , P. L. 1971 . Generalized Inverse Matrices , New York : Wiley-Interscience .
  • Engl , H. W. 1993 . Regularization methods for the stable solution of inverse problems . Surveys on Mathematics for Industry , 3 : 71 – 143 .
  • Trottenberg , U. , Oosterlee , C. and Schüller , A. 2001 . Multigrid , New York : Academic Press .
  • Nashed , M. Z. and Wahba , G. 1974 . Convergence rates of approximate least squares solutions of linear integral and operator equations of the first kind . Mathematics of Computation , 28 ( 125 ) : 69 – 80 .
  • Burden , R. L. and Faires , J. D. 2001 . Numerical Analysis , 7 , Pacific Grove, CA : Brooks/Cole .
  • Popa , C. 2006 . “ Kovarik-like algorithms for Tikhonov regularization of dense inverse problems. Technical Report ” . Friedrich-Alexander-Universität Erlangen-Nürnberg . 06–1, Lehrstuhl für Informatik 10 (Systemsimulation)

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.