Xiong Hui-jun
Abstract
An iterative method which is used to find the positive definite solution of the nonlinear matrix equation X+A~*X~(-n)A=I is constructed,where the matrix A is nonsingular and A~*A=AA~*.The convergence of the iterative method is proved under some conditions, and an error estimate formula is presented.
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An iterative method which is used to find the positive definite solution of the nonlinear matrix equation X+A~*X~(-n)A=I is constructed,where the matrix A is nonsingular and A~*A=AA~*.The convergence of the iterative method is proved under some conditions, and an error estimate formula is presented.
Key concepts: Invertible matrix, Iterative method, Convergence (economics), Mathematics, Matrix (chemical analysis), Applied mathematics, Nonlinear system, Positive-definite matrix