Iterative methods for the extremal positive definite solution of the matrix equation X+A*X-(alpha)A=Q star

作者：Peng, Zhen yun^*; El Sayed, Salah M; Zhang, Xiang lin

来源：Journal of Computational and Applied Mathematics, 2007, 200(2): 520-527.

DOI：10.1016/j.cam.2006.01.033

• positive definite matrix
• Matrix equation
• iterative method
• the maximal solution
• the minimal solution

In this paper, the inversion free variant of the basic fixed point iteration methods for obtaining the maximal positive definite solution of the nonlinear matrix equation X + A*X(-proportional to)A = Q with the case 0 < alpha <= I and the minimal positive definite solution of the same matrix equation with the case alpha >= 1 are proposed. Some necessary conditions and sufficient conditions for the existence of positive definite solutions for the matrix equation are derived. Numerical examples to illustrate the behavior of the considered algorithms are also given.

• 出版日期2007-3-15
• 单位湖南大学