不适定问题的迭代Tikhonov正则化方法  

ITERATED TIKHONOV REGULARIZATION FOR ILL-POSED PROBLEMS

作　　者：傅初黎[1] 李洪芳[1] 熊向团[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000

出　　处：《计算数学》2006年第3期237-246,共10页Mathematica Numerica Sinica

基　　金：国家自然科学基金(No.10271050);甘肃省自然科学基金(No.3ZS051-A25-015)资助课题;兰州大学理论物理与数学纯基础科学基金资助(No.Lzu05005).

摘　　要：Tikhonov正则化方法是研究不适定问题最重要的正则化方法之一,但由于这种方法的饱和效应,使得不可能随着解的光滑性假设的提高而提高收敛率,即不能使正则解与准确解的误差估计达到阶数最优．本文所讨论的迭代的Tikhonov正则化方法对此进行了改进,保证了误差估计总可以达到阶数最优．数值试验结果表明计算效果良好．Tikhonov regularization is one of the most important regularization methods for the study of ill-posed problems. But because of the saturation effect of this method it is impossible that the convergence rate can be improved with increasing smoothness assumption of solution, i.e., the error estimate between the exact and approximate solutions can not be order optimal. The iterated Tikhonov regulaxiza- tion prevent saturation effects, such that for any smoothness asumption the error estimate can always be order optimal for appropriate choice of iterated times.

关 键 词：不适定问题 TIKHONOV正则化 饱和效应 迭代Tikhonov正则化 

分 类 号：O241[理学—计算数学]