求解隐式迭代方程的多尺度配置法  

Multiscale collocation method for solving implicit iterative equations

作　　者：张荣 罗兴钧[2] 李丽君[2] ZHANG Rong;LUO Xingjun;LI Lijun(School of Data and Computer Science,Sun Yat-sen University,Guangzhou 510006,China;School of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,Jiangxi Province,China)

机构地区：[1]中山大学数据科学与计算机学院,广州510006 [2]赣南师范大学数学与计算机科学学院,江西赣州341000

出　　处：《应用数学与计算数学学报》2018年第3期472-485,共14页Communication on Applied Mathematics and Computation

基　　金：国家自然科学基金资助项目(11761010);江西省研究生创新专项资金资助项目(YC2015-S376)

摘　　要：用多尺度快速配置法求解病态积分方程的隐式迭代方程.在积分算子是扇形紧算子时,该方法得到了离散隐式迭代方程的近似解.采用Morozov偏差原理作为停止准则,并证明了在该准则下隐式迭代正则化方法所得近似解的收敛率.最后,用数值实验证实理论结果和说明数值方法的有效性.In the paper,the implicit iterative equation of the ill-posed integral equation is solved by the fast multiscale collocation method.When the integral operator is the sector compact operator,this method obtains the approximate solutions of the discrete implicit iterative equations.The convergence rate of the approximate solution obtained by the implicit iterative regularization method is proved by using the Morozov deviation principle as the stopping criterion.Finally,numerical experiments are presented to confirm the theoretical results and illustrate the efficiency of the method.

关 键 词：隐式迭代方程 扇形紧算子 近似解 Morozov偏差原理 

分 类 号：O242.2[理学—计算数学]