Solvability Theory and Iteration Method for One Self-Adjoint Polynomial Matrix Equation

Zhigang Jia, Meixiang Zhao, Minghui Wang, Sitao Ling
2014 Journal of Applied Mathematics  
The solvability theory of an important self-adjoint polynomial matrix equation is presented, including the boundary of its Hermitian positive definite (HPD) solution and some sufficient conditions under which the (unique or maximal) HPD solution exists. The algebraic perturbation analysis is also given with respect to the perturbation of coefficient matrices. An efficient general iterative algorithm for the maximal or unique HPD solution is designed and tested by numerical experiments.
doi:10.1155/2014/681605 fatcat:6ttjvxfbjbetdbn2mnei5oylwu