一种求解第一类Fredholm积分方程的改进Tikhonov正则化方法  

A modified Tikhonov Regularization Method for the Solution of Fredholm Equations of the First Kind

作　　者：郭家桥 张新明 马玲 GUO Jia-qiao;ZHANG Xin-ming;MA Ling(School of Science,Harbin Institute of Technology（Shenzhen）,Shenzhen 518055,China)

机构地区：[1]哈尔滨工业大学(深圳)理学院

出　　处：《数学的实践与认识》2018年第18期244-250,共7页Mathematics in Practice and Theory

基　　金：广东省自然科学基金(2017A030313280)

摘　　要：基于紧算子的奇异值系统理论，构造了一种新的正则化滤子函数，从而提出了一种改进的Tikhonov正则化方法，并且证明了解的收敛性及其渐进最优阶估计．通过两个数值算例，验证了改进Tikhonov正则化方法对于第一类Fredholm积分方程求解的有效性和优越性．In this work, based on the singular system of compact operator, a new regularizing filter function and a modified Tikhonov regularization method for the solution of Fredholm equation of the first kind were constructed. The convergence and the optimal asymptotic order of the regularized solution are proved. The numerical results demonstrate the effectiveness and the superiority of the modified Tikhonov regularization method.

关 键 词：第一类FREDHOLM积分方程 正则化滤子函数 改进Tikhonov正则化方法 渐进最优阶估计 

分 类 号：O175.5[理学—数学]