Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 88, 2011 - Issue 3
Submit an article Journal homepage
108
Views
7
CrossRef citations to date
0
Altmetric
Section B

An iterative method for the least squares solutions of the linear matrix equations with some constraint

Jing Cai School of Science, Huzhou Teachers College, Huzhou, Zhejiang, 313000, China; Department of Mathematics, East China Normal University, Shanghai, 200062, China
&
Guoliang Chen Department of Mathematics, East China Normal University, Shanghai, 200062, ChinaCorrespondence[email protected]
Pages 634-649 | Received 07 Aug 2009, Accepted 10 Jan 2010, Published online: 15 Dec 2010

References

  • Ben-Israel , A. and Greville , T. N.E. 2003 . Generalized Inverse: Theory and Applications , 69 – 95 . New York : Springer .
  • Chen , J. L. and Chen , X. H. 2001 . Special Matrices , Beijing : Tsinghua University Press .
  • Golub , G. H. , Nash , S. and Vanloan , C. 1979 . A Hessenberg–Schur method for the problem AX+XB=C . IEEE Trans. Auto. Control , 24 : 909 – 913 .
  • Higham , N. J. 1988 . Computing a nearest symmetric positive semidefinite matrix . Linear Algebra Appl. , 103 : 103 – 118 .
  • Horn , R. A. and Johnson , C. R. 1991 . Topics in Matrix Analysis , New York : Cambridge University Press .
  • Hou , J. J. , Peng , Z. Y. and Zhang , X. L. 2006 . An iterative method for the least square symmetric solution of matrix equation . Numer. Algor. , 42 : 181 – 192 .
  • Jeseph , K. T. 1992 . Inverse eigenvalue problem in structural design . AIAA J. , 30 : 2890 – 2896 .
  • Lei , Y. and Liao , A. P. 2007 . A minimal residual algorithm for the inconsistent matrix equation AXB=C over symmetric matrices . Appl. Math. Comput. , 188 ( 1 ) : 499 – 513 .
  • Liao , A. P. and Lei , Y. 2007 . Optimal approximate solution of the matrix equation AXB=C over symmetric matrices . J. Comput. Math. , 25 ( 5 ) : 543 – 552 .
  • Mitra , S. K. 1973 . Common solutions to a pair of linear matrix equations . Proc. Camb. Philos. Soc. , 74 : 213 – 216 .
  • Peng , Z. Y. 2005 . An iterative method for the least squares symmetric solution of the linear matrix equation AXB=C . Appl. Math. Comput. , 17 : 711 – 723 .
  • Peng , X. Y. , Hu , X. Y. and Zhang , L. 2006 . The orthogonal-symmetric or orthogonal-anti-symmetric least-square solutions of the matrix equation . Chin. J. Eng. Math. , 23 ( 6 ) : 1048 – 1052 .
  • Peng , Z. H. , Hu , X. Y. and Zhang , L. 2006 . An efficient algorithm for the least-squares reflexive solution of the matrix equation . Appl. Math. Comput. , 181 : 988 – 999 .
  • Piao , F. X. , Zhang , Q. L. and Wang , Z. F. 2007 . The solution to matrix equation . J. Fran. Inst. , 344 ( 8 ) : 1056 – 1062 .
  • Qiu , Y. Y. , ZHang , Z. Y. and Lu , J. F. 2007 . Matrix iterative solutions to the least squares problem of BXAT=F with some linear constraints . Appl. Math. Comput. , 185 : 284 – 300 .
  • Saad , Y. 2003 . Iterative methods for sparse linear systems , 2 , Philadelphia, PA : SIAM .
  • Sheng , X. P. and Chen , G. L. 2007 . A finite iterative method for solving a pair of linear matrix equations . Appl. Math. Comput./textit> , 189 : 1350 – 1358 .
  • Su , Y. F. and Chen , G. L. 2010 . Iterative methods for solving linear matrix equation and linear matrix system . Int. J. Comput. Math. , 87 ( 4 ) : 763 – 774 .
  • Wang , M. H. , Cheng , X. H. and Wei , M. S. 2007 . Iterative algorithms for solving the matrix equation . Appl. Math. Comput. , 187 ( 2 ) : 622 – 629 .
  • Yuan , Y. X. and Dai , H. 2008 . Generalized reflexive solutions of the matrix equation and associated optimal approximation problem . Comput. Math. Appl. , 56 : 1643 – 1649 .

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.