数值求解Symm积分方程的正则化MINRES方法  

Regularized MINRES Method for Solving the Symm Integral Equation

作　　者：吴颉尔[1] 戴华[2] 

机构地区：[1]南京航空航天大学理学院,南京210016 [2]江苏科技大学数理学院,镇江212003

出　　处：《工程数学学报》2008年第1期74-80,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10271055)

摘　　要：Symm积分方程在位势理论中具有重要应用,它是Hadamard意义下的不适定问题。离散该方程将产生对称线性不适定系统。基于GCV准则,并应用截断奇异值分解,本文提出数值求解Symm积分方程的正则化MINRES方法。与Tikhonov正则化方法相比,在数据出现噪声的情况下,新方法能有效地求得Symm积分方程的数值解。The Symm integral equation has an important application in potential theory, and is typically ill-posed in the sense of Hadamard. The discretization of such an equation gives rise to linear ill-posed problems. Based on the GCV criterion, a regularized MINRES method is presented to reconstruct the solution of the linear ill-posed problems by using truncated singular value decomposition. Compared with the Tikhonov regularization, the new method can reconstruct efficiently the regular solution of the Symm integral equation in the presence of noise or corrupted data.

关 键 词：Symm积分方程 Tikhonov 正则化 对称线性系统 MINRES方法 

分 类 号：O175.3[理学—数学]