| ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I |
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| 引用本文： | Yu-hai Zhang. ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A^＊X^-2 A=I[J]. 计算数学(英文版), 2005, 23(4): 408-418 |
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| 作者姓名： | Yu-hai Zhang |
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| 作者单位： | School of Mathematics and System Sciences, Shandong University, Jinan 250100, China |
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| 摘 要： | The Hermitian positive definite solutions of the matrix equation X-A^＊X^-2 A=I are studied. A theorem for existence of solutions is given for every complex matrix A. A solution in case A is normal is given. The basic fixed point iterations for the equation are discussed in detail. Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given.
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| 关 键 词： | 厄密共轭 正解 矩阵方程 迭代法 存在性 收敛性 |
| 收稿时间： | 2004-04-13 |
| 修稿时间： | 2004-04-132004-09-16 |
ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A*X~(-2)A=I |
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| Yu-hai;Zhang. ON HERMITIAN POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATION X-A*X~(-2)A=I[J]. Journal of Computational Mathematics, 2005, 23(4): 408-418 |
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| Authors: | Yu-hai Zhang |
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| Abstract: | The Hermitian positive definite solutions of the matrix equation X-A~*X~(-2)A=I are studied.A theorem for existence of solutions is given for every complex matrix A.A solution in case A is normal is given.The basic fixed point iterations for the equation are discussed in detail.Some convergence conditions of the basic fixed point iterations to approximate the solutions to the equation are given. |
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| Keywords: | Matrix equation Positive definite solution Iterative methods |
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