World Academy of Science, Engineering and Technology
Published March 3, 2014 | Version 9997855
Journal article Open

On the Positive Definite Solutions of Nonlinear Matrix Equation

Authors/Creators

Description

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δi are discussed. An algorithm that avoids matrix inversion with the case -1<-δi<0 is proposed.

Files

9997855.pdf

Files (144.0 kB)

Name Size Download all
md5:6cc83739bf6f850643e3ae1b68004b60
144.0 kB Preview Download

Additional details

References

  • V.I. Hasanov. "Positive definite solutions of the matrix equations ". Linear Algebra Appl. 2005, 404,pp. 166-182.
  • I.G. Ivanov. "On positive definite solutions of the family of matrix equations ". Compute. Appl. Math. 2006, 193 ,pp. 277-301.
  • X.Y. Yin, S.Y. Liu."Positive definite solutions of the matrix equations ". Computers and Mathematics with Applications. 2010, 59,pp. 3727-3739.
  • X. Duan, A. Liao, B. Tang. "On the nonlinear matrix equation ". Linear Algebra Appl. 2008,429,pp.110-121.
  • X. Duan, A. Liao. "On the existence of Hermitian positive definite solutions of the matrix equation ". Linear Algebra Appl. 2008, 429,pp. 673-687.
  • X.Y. Yin, S.Y. Liu, L. Fang. "Solutions and perturbation estimates for the matrix equations ". Linear Algebra Appl. 2009, 431 ,pp. 409-1421.
  • C.H. Guo. "Convergence rate of an iterative method for a nonlinear matrix equation". SIAM J. Matrix Anal . Appl. 2001, 23,pp. 295-302.
  • Z.Y. Peng, Salah M. El-Sayed, X.L. Zhang."Iterative methods for the extremal positive definite solution of the matrix equation ". Journal of Computational and mathematics. 2007, 200,pp. 520-527.
  • M. Monsalve, M. Raydan. "A new inversion-free method for a rational matrix equation". Linear Algebra Appl. 2010, 433,pp. 64-71. [10] A.M. Sarhan, Naglaa M.El-Shazly, Enas M. Shehata. "On the existence of extremal positive definite solutions of the nonlinear matrix equation ". Mathematical and Computer Modeling. 2010, 51,pp. 1107-1117. [11] R. Bhatia. Matrix analysis. Graduate Texts in Mathematics, Spring, Berlin, 1997. [12] X. Zhan. "Computing the extremal positive definite solutions of a matrix equation". SIAM J. Sci. Comput. 1996, 17,pp.1167-1174.