求解Lavrentiev迭代方程的多尺度快速配置算法  

Fast Multiscale Collocation Methods for Solving Iterated Lavrentiev Equations

作　　者：杨素华[1] 欧阳兆福 罗兴钧[1] 彭玉兵[1] 

机构地区：[1]赣南师范大学数学与计算机科学学院,江西赣州341000

出　　处：《数学年刊（A辑）》2017年第4期419-432,共14页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11361005;No.11761010;No.61502107);江西省自然科学基金(No.20151BAB201011);江西省研究生创新基金(No.YC2015-S376)的资助

摘　　要：考虑了第一类Fredholm积分方程的求解.采用有矩阵压缩策略的多尺度配置方法来离散Lavrentiev迭代方程,在积分算子是弱扇形紧算子时,给出近似解的先验误差估计,并给出了改进的后验参数的选择方法,得到了近似解的收敛率.最后,举例说明算法的有效性.The authors consider ill-posed Fredholm integral equations of the first kind. The authors apply a multiscale collocation method with a matrix compression strategy to discretize the iterated Lavrentiev equation and then analyze the priori convergence of the multiscale collocation method, if the integral operator is the weakly sectorial operator. The convergence rates of the iterated Lavrentiev regularization are achieved by using a modified a posteriori parameter choice strategy. Finally, numerical examples are given to illustrate the efficiency of the method.

关 键 词：第一类FREDHOLM积分方程 迭代Lavrentiev正则化方法 多尺度配置法 后验参数选择策略 

分 类 号：O241.83[理学—计算数学]