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| 解第一类算子方程的一种迭代正则化方法 | |
| 引用本文： | 冯立新,刘松树. 解第一类算子方程的一种迭代正则化方法[J]. 应用数学学报, 2011, 34(3) |
| 作者姓名： | 冯立新 刘松树 |
| 作者单位： | 1. 黑龙江大学数学学院,哈尔滨,150080 2. 哈尔滨工业大学数学系,哈尔滨,150080 |
| 基金项目： | 国家自然科学基金，黑龙江省教育厅项目，黑龙江大学创新团队项目 |
| 摘 要： | 提出了一种求解第一类算子方程的新的迭代正则化方法,并依据广义Arcangeli方法选取正则参数,建立了正则解的收敛性.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. |
| 关 键 词： | 第一类算子方程 不适定问题 迭代正则化方法 广义Arcangeli方法 |
A Method of Iterated Regularization for Operator Equation of the First Kind |
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| FENG LIXIN,LIU SONGSHU. A Method of Iterated Regularization for Operator Equation of the First Kind[J]. Acta Mathematicae Applicatae Sinica, 2011, 34(3) | |
| Authors: | FENG LIXIN LIU SONGSHU |
| Affiliation: | FENG Lixin (Department of Mathematics,Heilongjiang University,Harbin 150080) LIU SONGSHU (Department of Mathematics,Harbin Institute of Technology,Harbin 150080) |
| Abstract: | The paper presents a new method of iterated regularization for solving operation equation of the first kind,and by applying the generalized Arcangeli's criterion of choose the regularization parameter,we obtain the convergence of the regularized solution,and as compared with Tikhonov regularization,the asymptotic order of regularized solution is improved. |
| Keywords: | operator equation of the first kind ill-posed problem iterative regularization method generalized Arcangeli's criterion |
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