|
|||||
|
|
| 求解病态问题的一种改进的Tikhonov正则化--(1)正则化方法的建立 | |
| 引用本文： | 王家军,李功胜. 求解病态问题的一种改进的Tikhonov正则化--(1)正则化方法的建立[J]. 数学季刊, 2000, 15(2) |
| 作者姓名： | 王家军 李功胜 |
| 作者单位： | 新乡师范专科学校数学系!河南新乡453000(王家军)，西安交通大学理学院!陕西西安710049(李功胜) |
| 摘 要： | 对于带有右端扰动数据的第一类紧算子方程的病态问题 ,本文应用正则化子建立了一类新的正则化求解方法 ,称之为改进的Tikonov正则化 ;通过适当选取正则参数 ,证明了正则解具有最优的渐近收敛阶 .与通常的Tikhonov正则化相比 ,这种改进的正则化可使正则解取到足够高的最优渐近阶 |
| 关 键 词： | 病态问题 改进的Tikhonov正则化 正则解的收敛性与渐近阶 |
A Modified Tikhonov Regularization Method for Solving Ill-posed Problems--(1)Constroution of Regularization |
|
| WANG Jia-jun,LI Gong-sheng. A Modified Tikhonov Regularization Method for Solving Ill-posed Problems--(1)Constroution of Regularization[J]. Chinese Quarterly Journal of Mathematics, 2000, 15(2) | |
| Authors: | WANG Jia-jun LI Gong-sheng |
| Abstract: | In this paper, a new class of improved regularization methods, called modified Tikhonov regularization (MTR) for solving ill_posed problems of the first kind of operator equation with noisy data is constructed. By a priori choosing regularization parameter, optimal convergence order of the regularized solution is obtained. As compared with ordinary Tikhonov regularization (OTR), this new scheme can achieve higher optimum asymptotic order of the regularized solution by selecting an auxiliary parameter. |
| Keywords: | ill_posed problem modified Tikhonov regularization convergence and asymptotic order of the regularized solution |
| 本文献已被 CNKI 万方数据 等数据库收录！ | |