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International Journal of Computer Mathematics Volume 82, 2005 - Issue 7
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Original Articles

Necessary and sufficient conditions for the existence of positive definite solutions of the matrix equation X+ATX−2A=I

Mohamed A. Ramadan Department of Mathematics, Faculty of Science, Menoufia University, EgyptCorrespondence[email protected]
Pages 865-870 | Received 23 Apr 2004, Published online: 25 Jan 2007

References

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  • Ivanov , I. G. and El-Sayed , S. M. 1998 . Properties of positive definite solutions of the equation X + A*X-2A = I . Linear Algebra Applications , 279 : 303 – 316 .
  • Engwerda , J. C. 1993 . On the existence of a positive definite solution of the matrix equation . Linear Algebra Applications , 194 : 91 – 108 .
  • El-Sayed , S. M. and Ramadan , M. A. 2001 . On the existence of a positive definite solution of the matrix equation . International Journal of Computer Mathematics , 76 : 331 – 338 .
  • Chun-Hua , G. and Lancaster , P. 1999 . Iterative solution of two matrix equations . Mathematics of Computation , 68 ( 228 ) : 1589 – 1603 .
  • Zhan , X. 1996 . Computing the extremal positive definite solutions of a matrix equation . SIAM Journal on Scientific Computing , 17 : 1167 – 1174 .
  • Meini , B. 2001 . Efficient computation of the extreme solutions of and . Mathematics of Computation , 71 : 1189 – 1204 .
  • Zhan , X. and Xie , J. 1996 . On the matrix equation: . Linear Algebra Applications , 247 : 337 – 345 .
  • Xu , S. F. 2001 . Perturbation analysis of the maximal solution of the matrix equation: . Linear Algebra Applications , 336 : 61 – 70 .
  • Golub , G. H. and Van Loan , C. F. Matrix Computations , Baltimore, MD : Johns Hopkins University Press .

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