Advanced search
Publication Cover
International Journal of Computer Mathematics Volume 80, 2003 - Issue 12
Submit an article Journal homepage
56
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

An algorithm for computing positive definite solutions of the nonlinear matrix equation X + A*X−1A = I

Salah M. El-SayedCorrespondence[email protected]
Pages 1527-1534 | Received 13 Jan 2003, Published online: 12 May 2010

References

  • Anderson , W. N. Jr. , Morley , T. D. and Trapp , G. E. (1990) . Positive solution to X = A − BX −1 B* . Linear Algebra Appl. , 134 : 53 – 62 .
  • Engwerda , J. C. , Andre Ran , C. M. and Rijkeboer , A. L. (1993) . Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X + A*X −1 A = Q . Linear Algebra Appl. , 186 : 255 – 275 .
  • Engwerda , J. C. (1993) . On the existence of a positive definite solution of the matrix equation X + A T X −1 A = I . Linear Algebra Appl. , 194 : 91 – 108 .
  • Guo , C.-H. and Lancaster , P. (1999) . Iterative solution of two matrix equations . The Mathematics of Computation , 68 : 1589 – 1603 .
  • Ivanov , I. G. and El-Sayed , S. M. (1998) . Properties of positive definite solutions of the equation X + A*X −2 A = I . Linear Algebra and Appl. , 279 : 303 – 316 .
  • Lancaster P. Rodman L. Algebraic Riccati Equations Clarendon Press Oxford (1995)
  • Lancaster P. Theory of Matrices Academic Press New York (1969)
  • El-Sayed , S. M. (2001) . On the two iterations processes for computing positive definite solutions of the matrix equation X − A*X −n A = I . Computers & Mathematics with Appl. , 41 : 579 – 588 .
  • El-Sayed , S. M. and Andre Ran , C. M. (2001) . On the iteration methods for solving a class of nonlinear matrix equations . SIAM J. Matrix Anal. Appl. , 23 : 632 – 645 .
  • El-Sayed , S. M. and Ramadan , M. A. (2001) . On the existence of a positive definite solution of the matrix equation . Inter. J. Comput. Math. , 76 : 331 – 338 .
  • El-Sayed , S. M. and El-Alem , M. (2002) . Some properties for the existence of a positive definite solution of matrix equation X + A*X −2 m A = I . Appl. Math. Comput. , 128 ( 1 ) : 99 – 108 .
  • El-Sayed , S. M. (2003) . Two sided iteration methods for computing positive definite solutions of a nonlinear matrix equation . J. Australian Mathematical Society, Series B , 45 : 145 – 152 .
  • Zhan , X. and Xie , J. (1996) . On the matrix equation X + A*X −1 A = I . Linear Algebra Appl. , 247 : 337 – 345 .
  • Zhan , X. (1996) . Computing the extremal positive definite solutions of a matrix equation . SIAM J. Sci. Comput. , 17 : 1167 – 1174 .

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.