Positive Definite Solution of Two Kinds of Nonlinear Matrix Equations
نویسندگان
چکیده
Based on the elegant properties of the Thompson metric, we prove that the following two kinds of nonlinear matrix equations X = m ∑ i=1 AiX iAi and X = m ∑ i=1 (AiXAi) δi , (0 < |δi| < 1) always have a unique positive definite solution. Iterative methods are proposed to compute the unique positive definite solution. We show that the iterative methods are more effective as δ = max{|δi|, i = 1, 2, · · · ,m} decreases. Perturbation bounds for the unique positive definite solution are derived in the end. Full text
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تاریخ انتشار 2010