Hermitian Positive Definite Solution of the Matrix Equation X=Q+∑i=1mAi(B+X-1)-1Ai*. (24th September 2014)

• Record Type: Journal Article
• Authors: Li, Chun-Mei; Peng, Jing-Jing
• Other Names: Asaithambi Asai Academic Editor.
• Is Part Of: International journal of computational mathematics. Volume 2014(2014)
• Publication Date: 2014-09-24
• Subjects: Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Periodicals; 518.05
• DOI: 10.1155/2014/727093
• Languages: English
• ISSNs: 2356-797X

Abstract

Abstract : We consider the Hermitian positive definite solution of the nonlinear matrix equation X = Q + ∑ i = 1 m A i ( B + X - 1 ) - 1 A i * . Some new sufficient conditions and necessary conditions for the existence of Hermitian positive definite solutions are derived. An iterative method is proposed to compute the Hermitian positive definite solution. In the end, an example is used to illustrate the correctness and application of our results.