Positive Definite Solutions of Operator Equations X m + A * X - n A = I |
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| Authors: | Shuanping Du Jinchuan Hou |
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| Affiliation: | a Department of Mathematics, Shanxi University, Taiyuan, 030000; Department of Mathematics, Shanxi Teachers University, Linfen, 041004, P. R. China.b Department of Mathematics, Shanxi Teachers University, Linfen, 041004, P. R. China. |
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| Abstract: | In this article, we discuss the positive definite solutions of the operator equation X m + A * X -n A = I , , on a Hilbert space. Necessary and sufficient conditions for the existence of a positive semi-definite solution are derived. Under some conditions, two effective iterative methods for getting a positive definite solution of this equation are proposed and error estimations are obtained. |
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| Keywords: | Operator Equations Positive Operators Isometric Operators |
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