Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 93, 2016 - Issue 7
Submit an article Journal homepage
194
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

The right–left preconditioning technique for the solution of the large matrix equation AXB = C

Saeed KarimiDepartment of Mathematics, Persian Gulf University, Bushehr75169, IranCorrespondence[email protected]
Pages 1226-1239 | Received 22 Jan 2014, Accepted 21 Mar 2015, Published online: 26 May 2015

References

  • Z.-Z. Bai, On Hermitian and skew-Hermitian splitting iteration methods for continuous Sylvester equations, J. Comput. Math. 29 (2011), pp. 185–198.
  • U. Baur and P. Benner, Cross-Gramian based model reduction for data-sparse systems, Electron. Trans. Numer. Anal. 31 (2008), pp. 256–270.
  • A. Bouhamedi, K. Jbilou, L. Reichel, and H. Sadok, An extrapolated TSVD method for linear discrete ill-posed problems with Kronecker structure, Linear Algebra Appl. 434 (2011), pp. 1677–1688. doi: 10.1016/j.laa.2010.06.001
  • A. Björck, Numerical Methods for Least Squares Problems, SIAM, Phildelphia, PA, 1996.
  • D. Calvetti and L. Reichel, Application of ADI iterative methods to the restoration of noisy images, SIAM J. Matrix Anal. Appl. 17 (1996), pp. 165–186. doi: 10.1137/S0895479894273687
  • B. Datta, Numerical Methods for Linear Control Systems, Elsevier, New York, 2004.
  • Y.-B. Deng, Z.-Z. Bai, and Y.-H. Gao, Iterative orthogonal direction methods for Hermitian minimum norm solution of two consistent matrix equations, Numer. Linear Algebra Appl. 13 (2006), pp. 801–823. doi: 10.1002/nla.496
  • F. Ding, P.- X. Liu, and J. Ding, Iterative solutions of the generalized Sylvester matrix equation by using hierarchical identification principle, Appl. Math. Comput. 197 (2008), pp. 41–50. doi: 10.1016/j.amc.2007.07.040
  • A. El Guennouni, K. Jbilou, and J. Riquet, Block Krylov subspace methods for solving large Sylvester equation, Numer. Algorithms 29 (2002), pp. 75–96. doi: 10.1023/A:1014807923223
  • S. Karimi and B. Zali, The block preconditioned LSQR and GL-LSQR algorithms for the block partitioned matrices, Appl. Math. Comput. 227 (2014), pp. 811–820. doi: 10.1016/j.amc.2013.11.039
  • M. Khorsand Zak and F. Toutounian, Nested splitting conjugate gradient method for matrix equation AXB=C and preconditioning, Comput. Math. Appl. 66 (2013), pp. 269–278. doi: 10.1016/j.camwa.2013.05.004
  • A.-P. Liao, Z.-Z. Bai, and Y. Lei, Best approximate solution of matrix equation AXB+CYD=E, SIAM J. Matrix Anal. Appl. 27 (2005), pp. 675–688. doi: 10.1137/040615791
  • Matrix Market. Available at http//math.nist.gov/Matrix Market, October 2002.
  • C.-C. Paige and M.-A. Saunders, LSQR: An algorithm for sparse linear equations and sparse least squares, ACM Trans. Math. Software. 8 (1982), pp. 43–71. doi: 10.1145/355984.355989
  • D.-K. Salkuyeh, CG-type algorithms to solve symmetric matrix equations, Appl. Math. Comput. 172 (2006), pp. 985–999. doi: 10.1016/j.amc.2005.03.003
  • D.-K. Salkuyeh and F. Toutounian, New approaches for solving large Sylvester equations, Appl. Math. Comput. 173 (2006), pp. 9–18. doi: 10.1016/j.amc.2005.02.063
  • F. Toutounian and S. Karimi, Global least squares method (GL-LSQR) for solving general linear systems with several right-hand sides, Appl. Math. Comput. 178 (2006), pp. 452–460. doi: 10.1016/j.amc.2005.11.065
  • M. Wang and Y. Feng, An iterative algorithm for solving a class of matrix equations, J. Control Theory Appl. 7 (2009), pp. 68–72. doi: 10.1007/s11768-009-6124-8
  • L. Xie, J. Ding, and F. Ding, Gradient based iterative solutions for general linear matrix equations, Comput. Math. Appl. 58 (2009), pp. 1441–1448. doi: 10.1016/j.camwa.2009.06.047

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.