| 算子方程X+A~*X~(-t)A=Q的正算子解的研究 |
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| 引用本文： | 杨凯凡.算子方程X+A~*X~(-t)A=Q的正算子解的研究[J].数学的实践与认识,2012,42(4):217-221. |
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| 作者姓名： | 杨凯凡 |
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| 作者单位： | 陕西理工学院数学与计算机科学学院,陕西汉中,723000 |
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| 摘 要： | 研究了算子方程X+A*X~(-t)A=Q(t>1)的正算子解问题,分别给出了算子方程X+A*X~(-t)A=Q有正算子解的一些充分条件和必要条件,并确定了解的范围,用迭代的方法得到方程的正算子解.
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| 关 键 词： | 算子方程 正算子 迭代法 谱半径 |
Studies on the Positive Operator Solutions to Operator Equations X + A*X-tA =Q |
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| YANG Kai-fan.Studies on the Positive Operator Solutions to Operator Equations X + A*X-tA =Q[J].Mathematics in Practice and Theory,2012,42(4):217-221. |
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| Authors: | YANG Kai-fan |
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| Institution: | YANG Kai-fan (College of Mathematics and Computer Science,Shaanxi University of Technology,Hanzhong 723000,China) |
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| Abstract: | In this paper,the positive operator solutions to the operator equation X+ A*X-tA=Q（t>1） is studied.The necessary conditions and sufficient conditions for the existence of positive operator solutions to the operator equation X + A*X-tA = Q are derived respectively.Also,the range of the solutions is determined.An iterative method for finding the positive operator solutions is construsted. |
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| Keywords: | operator equation positive operator iterative method spectral radius |
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