| 非线性矩阵方程X-A*((X)-C)-n A=Q的正定解 |
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| 引用本文： | 刘巍,王柏育,熊慧军.非线性矩阵方程X-A*((X)-C)-n A=Q的正定解[J].阜阳师范学院学报(自然科学版),2011,28(1):8-10. |
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| 作者姓名： | 刘巍 王柏育 熊慧军 |
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| 作者单位： | 长沙学院信息与计算科学系;湖南大学数学与计量经济学院; |
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| 基金项目： | 湖南省教育厅基金资助科研项目(09C117); 长沙学院科学研究基金项目(CDJJ-07010204)资助 |
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| 摘 要： | 研究了非线性矩阵方程X-A*((X)-C)-n A=Q的正定解,证明了该方程一定存在正定解,并给出了正定解的存在区间、存在唯一正定解的条件以及迭代求解方法.
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| 关 键 词： | 非线性矩阵方程 正定解 迭代方法 |
Positive definite solution of nonlinear matrix equation |
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| LIU Wei,WANG Bai-yu,XIONG Hui-jun.Positive definite solution of nonlinear matrix equation[J].Journal of Fuyang Teachers College:Natural Science,2011,28(1):8-10. |
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| Authors: | LIU Wei WANG Bai-yu XIONG Hui-jun |
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| Institution: | LIU Wei1,WANG Bai-yu2,XIONG Hui-jun1(1.Department of Information and Computing Science,Changsha College,Changsha Hunan 410003,China,2.School of Mathematics and Econometrics,Hunan University,Changsha Hunan 410082,China) |
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| Abstract: | The positive definite solutions of the nonlinear matrix equation are studied.A theorem for the existence of the positive definite solution is proved.Furthermore,the bounds of the solutions,a sufficient condition for this equation to have unique positive definite solution and some computing methods are given. |
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| Keywords: | nonlinear matrix equations positive definite solution iteration method |
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