An improved inversion-free method for solving the matrix equation X + A*X(-alpha)A = Q

作者：Zhang, Li^*

来源：Journal of Computational and Applied Mathematics, 2013, 253: 200-203.

DOI：10.1016/j.cam.2013.04.007

• Damped Newton method
• Inversion-free method
• Fixed point method
• Convergence

In this paper, based on the damped Newton method, we present an inversion-free iterative method with a stepsize parameter for solving the nonlinear matrix equation X+A*X(-alpha)A = Q, where Q is a Hermitian positive definite matrix and alpha >= 1. The proposed method is an extension of Algorithm 2.2 in [Z. Peng, S.M. El-Sayed, X. Zhang, Iterative methods for the extremal positive definite solution of the matrix equation X+A*X(-alpha)A = Q, J. Comput. Appl. Math. 200 (2007) 520-527]. Preliminary numerical results show that the proposed method can improve numerical effect.

• 出版日期2013-12-1
• 单位长沙理工大学