| 扰动数据具有附加性质的Tikhonov正则化的某些方法 |
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| 引用本文： | 贺国强,尹秀玲. 扰动数据具有附加性质的Tikhonov正则化的某些方法[J]. 上海大学学报(英文版), 2007, 11(2): 126-131. DOI: 10.1007/s 11741-007-0207-x |
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| 作者姓名： | 贺国强 尹秀玲 |
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| 作者单位： | Department of Mathematics.College of Sciences Shanghai University，Department of Mathematics.College of Sciences，Shanghai University，Shanghai 200444，P.R.China，Shanghai 200444，P.R.China |
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| 摘 要： | In this paper, the Tikhonov regularization method was used to solve the nondegenerate compact hnear operator equation, which is a well-known ill-posed problem. Apart from the usual error level, the noise data were supposed to satisfy some additional monotonic condition. Moreover, with the assumption that the singular values of operator have power form, the improved convergence rates of the regularized solution were worked out.
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| 关 键 词： | 扰动数据 Tikhonov正则化方法 单调条件 收敛 不适定性方程 |
| 收稿时间： | 2005-01-24 |
| 修稿时间： | 2005-04-27 |
Some studies on the Tikhonov regularization method with additional assumptions for noise data |
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| HE Guo-qiang,YIN Xiu-ling. Some studies on the Tikhonov regularization method with additional assumptions for noise data[J]. Journal of Shanghai University(English Edition), 2007, 11(2): 126-131. DOI: 10.1007/s 11741-007-0207-x |
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| Authors: | HE Guo-qiang YIN Xiu-ling |
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| Affiliation: | Department of Mathematics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China |
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| Abstract: | In this paper,the Tikhonov regularization method was used to solve the nondegenerate compact linear operator equation,which is a well-known ill-posed problem.Apart from the usual error level,the noise data were supposed to satisfy some additional monotonic condition.Moreover,with the assumption that the singular values of operator have power form, the improved convergence rates of the regularized solution were worked out. |
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| Keywords: | ill-posed equation Tikhonov regularization method monotonic condition convergence rates |
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