Chebyshev多项式过滤子方法求解Poisson方程未知源问题  

Chebyshev polynomial regularization method for solving the unknown source on Poisson equation

作　　者：代佩 熊向团 DAI Pei;XIONG Xiangtuan(College of Mathematics and Statistics,Northwest Normal University Lanzhou 730050,China)

机构地区：[1]西北师范大学数学与统计学院

出　　处：《南昌大学学报（理科版）》2019年第5期421-428,共8页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(11661072);西北师范大学科学计算创新团队项目(NWNU-LKQN-17-5)

摘　　要：Poisson方程未知源识别问题是一类重要的不适定问题.由于经典Tikhonov正则化方法具有饱和效应,采用Chebyshev多项式过滤子方法给出其近似解。并且分别在先验和后验正则化参数选取规则下给出其相应的近似解的最优阶误差估计。The problem of determining unknown source on Poisson equation is a severely ill-posed problem.Because the standard Tikhonov regularization method has saturation restriction,in this paper,to obtain the regularization solution for the unknown source,using Chebyshev polynomial regularization method.And the error estimates under an a priori parameter choice rule and an a posteriori parameter choice rule are proved,respectively.

关 键 词：未知源识别 不适定问题 Chebyshev多项式过滤子方法 收敛阶数 

分 类 号：O241.8[理学—计算数学]