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Matrix equation problem is one of the topics of active research in the context of computational mathematics. The Hermitian positive definite solutions of a matrix equation play an important role in real applications. In this paper, we present the sufficient conditions for the existence of the positive definite solution to the nonlinear matrix equation X - A* (X-1)1/2 A = I and propose a natural and stable iteration algorithm for obtaining a positive definite solution of this matrix equation. Finally, two numerical examples for the convergence behavior of the proposed algorithm are conducted to demonstrate the effectiveness.
Date of Conference: 15-19 April 2011