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

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.