| 紧算子方程的不适定性分析及其在一维热传导反问题中的应用 |
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| 引用本文： | 闵涛,葛宁国,张敏,张帆.紧算子方程的不适定性分析及其在一维热传导反问题中的应用[J].应用泛函分析学报,2012(2):140-146. |
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| 作者姓名： | 闵涛 葛宁国 张敏 张帆 |
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| 作者单位： | 西安理工大学理学院 |
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| 基金项目： | 陕西省教育厅基金(08JK388) |
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| 摘 要： | 对紧算子方程的不适定性进行了详细的分析,证明了紧算子方程奇异值分解定理,并以一维热传导方程反问题为例,将其转化为紧算子方程,讨论了求解此反问题的最优估计及进行了误差分析,数值模拟表明了理论分析与实际应用的一致性.
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| 关 键 词： | 紧算子 反问题 不适定 正则化 正则参数 |
Ill-Posedness of Compact Operator Equation and Its Application in One-Dimensional Backward Heat Conduction Problem |
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| MIN Tao,GE Ningguo,ZHANG Min,ZHANG Fan.Ill-Posedness of Compact Operator Equation and Its Application in One-Dimensional Backward Heat Conduction Problem[J].Acta Analysis Functionalis Applicata,2012(2):140-146. |
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| Authors: | MIN Tao GE Ningguo ZHANG Min ZHANG Fan |
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| Institution: | School of Sciences,Xi ’an University of Technology,Xi ’an 710054,China |
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| Abstract: | The purpose of the paper is to discuss the ill-posedness and to prove the singular value decomposition theorem of compact operator equation.Then taking one-dimensional backward heat conduction problem for example,we translate it into compact operator equation and put forward an optimal estimate of which error analysis is also given for solving the ill-posed problem.Numerical simulation shows that the theoretical analysis is consistent with practical application. |
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| Keywords: | compact operator inverse problem ill-posed regularization regular parameter |
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