Recursive Solutions of the Matrix Equations X + ATX − 1 A = Q and X − ATX − 1 A = Q
نویسنده
چکیده
Abstract Two classes of recursive algorithms for computing the extreme solutions of the matrix equations X+AT X−1A = Q and X−AT X−1A = Q are presented. The Per Step Algorithms are based on the fixed point iteration method and its variations; the proposed Per Step Algorithm is an inversion free variant of the fixed point iteration method. The Doubling Algorithms are based on the cyclic reduction method and the Riccati equation solution method; the proposed Doubling Algorithm uses recursive solutions of the corresponding Riccati equations to solve any of the above matrix equations. Simulation results are given to illustrate the efficiency of the proposed algorithms.
منابع مشابه
The Matrix Equation X+ATX-1A=Q and Its Application in Nano Research
The matrix equation X + ATX−1A = Q has been studied extensively when A and Q are real square matrices and Q is symmetric positive definite. The equation has positive definite solutions under suitable conditions, and in that case the solution of interest is the maximal positive definite solution. The same matrix equation plays an important role in Green’s function calculations in nano research, ...
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