The Hermitian Positive Definite Solution of the Nonlinear Matrix Equation

作者：Zhang, Xindong^*; Feng, Xinlong

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2017, 18(5): 293-301.

DOI：10.1515/ijnsns-2016-0016

• Hermitian positive definite solution
• nonlinear matrix equation
• iterative algorithm

In this paper, we study the nonlinear matrix equation X-s +/- Sigma(m)(i=1) A(i)(T) X-delta i A(i) = Q, where A(i) (i = 1,2,..., m) is n x n nonsingular real matrix and Q is n x n Hermitian positive definite matrix. It is shown that the equation has an unique Hermitian positive definite solution under some conditions. Iterative algorithms for obtaining the Hermitian positive definite solution of the equation are proposed. Finally, numerical examples are reported to illustrate the effectiveness of algorithms.

• 出版日期2017-8
• 单位新疆大学; 新疆师范大学