| 解算子与右端数据均有扰动的半正定算子方程的动态系统方法 |
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| 引用本文： | 罗兴钧,陈仲英.解算子与右端数据均有扰动的半正定算子方程的动态系统方法[J].数学年刊A辑(中文版),2006(3). |
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| 作者姓名： | 罗兴钧 陈仲英 |
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| 作者单位： | 赣南师范学院数学与计算机系，中山大学科学计算与计算机应用系 江西 赣州 341000，广州 510275 |
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| 基金项目： | 国家自然科学基金(No．10371137，No．10201034)，高等学校博士学科点专项基金(No．20030558008)，广东省自然科学基金(No．05003308)，中山大学高等学术研究基金资助的项目 |
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| 摘 要： | 本文研究了求解算子与右端数据均有扰动的第一类半正定算子方程的动态系统方法．证明了相应的动态系统Cauchy问题的整体解存在且收敛于原算子方程的解．此外,给出了解Cauchy问题的迭代方法并证明了方法的收敛性．
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| 关 键 词： | 不适定问题 动态系统方法 算子方程 |
Dynamical Systems Method for Positive Semi-definite Operator Equations with Perturbed Operator and Nonexact Right-Hand |
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| LUO Xingjun CHEN Zhongying.Dynamical Systems Method for Positive Semi-definite Operator Equations with Perturbed Operator and Nonexact Right-Hand[J].Chinese Annals of Mathematics,2006(3). |
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| Authors: | LUO Xingjun CHEN Zhongying |
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| Abstract: | The dynamical system method is studied for solving operator equations of the first kind involving positive semi-definite operator with both operator and right-hand non- exact.This method consists of solving a Cauchy problem for a linear operator equation.It is proved that the problem has a global solution whose limit at infinity solves the original equation.Moreover,two convergent iterative processes are presented for the Cauchy problem of the dynamical system. |
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