应用改进的Tikhonov正则化求解Symm积分方程的数值分析  

Numerical Analysis on Solving Symm’s Integral Equation with a Modified Tikhonov Regularization Algorithm

作　　者：李功胜[1] 马逸尘[2] 

机构地区：[1]山东理工大学数学学院应用数学所,淄博255049 [2]西安交通大学理学院,西安710049

出　　处：《工程数学学报》2004年第5期825-828,768,共5页Chinese Journal of Engineering Mathematics

基　　金：山东省自然科学基金(Y2001E03);山东省高校中青年学术骨干基金资助项目.

摘　　要：应用一种改进的Tikhonov正则化,探讨了算子与右端数据都有扰动情形下Symm积分方程的数值求解。与通常的Tikhonov正则化相比,这种改进的正则化算法提高了正则解的渐近阶。A modified Tikhonov regularization is applied to solve a Symm’s integral equation with perturbed operators and noisy data, and some numeircal analyses are presented. As compared with ordinary Tikhonov regularization, this new scheme can not only improve the asymptotic convergence order of the regularized solution, but also relatively reduce the computational complexity.

关 键 词：Symm积分方程 改进的Tikhonov正则化 数值分析 渐近阶 

分 类 号：O175.3[理学—数学]