IDEAS home Printed from
MyIDEAS: Login to save this paper or follow this series

A framework of conjugate direction methods for symmetric linear systems in optimization

  • Giovanni Fasano


    (Dept. of Management, Università Ca' Foscari Venice)

In this paper we introduce a parameter dependent class of Krylov-based methods, namely CD, for the solution of symmetric linear systems. We give evidence that in our proposal we generate sequences of conjugate directions, extending some properties of the standard Conjugate Gradient (CG) method, in order to preserve the conjugacy. For specific values of the parameters in our framework we obtain schemes equivalent to both the CG and the scaled-CG. We also prove the finite convergence of the algorithms in CD, and we provide some error analysis. Finally, preconditioning is introduced for CD, and we show that standard error bounds for the preconditioned CG also hold for the preconditioned CD.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: First version, 2013
Download Restriction: no

Paper provided by Department of Management, Università Ca' Foscari Venezia in its series Working Papers with number 31.

in new window

Length: 36 pages
Date of creation: Dec 2013
Date of revision:
Handle: RePEc:vnm:wpdman:67
Contact details of provider: Postal: San Giobbe, Cannaregio 873, 30121 Venezia
Phone: +39 0412348721
Fax: +39 0412348701
Web page:

More information through EDIRC

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Giovanni Fasano & Massimo Roma, 2013. "Preconditioning Newton–Krylov methods in nonconvex large scale optimization," Computational Optimization and Applications, Springer, vol. 56(2), pages 253-290, October.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:vnm:wpdman:67. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco LiCalzi)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.