| 解第一类算子方程的一种新的正则化方法 |
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| 引用本文： | 杨宏奇,侯宗义. 解第一类算子方程的一种新的正则化方法[J]. 数学学报, 1997, 40(3): 369-376. DOI: cnki:ISSN:0583-1431.0.1997-03-007 |
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| 作者姓名： | 杨宏奇 侯宗义 |
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| 作者单位： | 复旦大学数学研究所 |
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| 摘 要： | 对算子与右端都为近似给定的第一类算子方程提出一种新的正则化方法，依据广义Ａｒｃａｎｇｅｌｉ方法选取正则参数，建立了正则解的收敛性。这种新的正则化方法与通常的Ｔｉｋｈｏｎｏｖ正则化方法相比较，提高了正则解的渐近阶估计。
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| 关 键 词： | 第一类算子方程，正则化方法，广义Arcangeli方法，正则解的收敛性，正则解的渐近阶 |
| 收稿时间： | 1995-09-20 |
A New Regularization Method for the Operator Equation of the First Kind |
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| Yang Hongqi Hou Zongyi. A New Regularization Method for the Operator Equation of the First Kind[J]. Acta Mathematica Sinica, 1997, 40(3): 369-376. DOI: cnki:ISSN:0583-1431.0.1997-03-007 |
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| Authors: | Yang Hongqi Hou Zongyi |
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| Affiliation: | Yang Hongqi Hou Zongyi ( Mathematics Institute, Fudan University, Shanghai 200433, China) |
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| Abstract: | In this paper, we present a new regularization method for solving t he operator equation of the first kind with approximate operator and the right-hand side. By applying the generalized Arcangeli's criterion to choose the regularization parameter, we obtain the convegence of the regularized solution, and as compared with Tikhonov regularization , the asymptotic order of tbe regularized solution is improved . |
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| Keywords: | Operator equation of the first kind Regularization method Generalized Arcangeli's criterion Convergence and asymptotic order of the regularized solution |
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