弱奇异紧积分算子多尺度Petrov-Galerkin谱逼近  

Spectral approximation of compact integral operators with weak singular kernel by using multiscale Petrov-Galerkin method

作　　者：唐帅[1,2] 姬小龙[1] 

机构地区：[1]济源职业技术学院基础部,河南济源459000 [2]广西师范学院数学科学学院,广西南宁530023

出　　处：《兰州理工大学学报》2016年第6期156-159,共4页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金数学天元基金(11326232)

摘　　要：讨论紧积分算子特征值问题的一种多尺度快速算法,针对具有弱奇异性积分算子的情形,考虑采用多尺度Petrov-Galerkin法进行求解.在此基础上,给出一种矩阵的压缩策略,发现可以大大降低计算量,并证明通过选取适当的截断参数,算法可以获得谱逼近的最优收敛阶.A fast multiscale algorithm for solving eigenvale problem of compact integral is discussed. Aimed at the case of integral operator with weak singularity, the fast multiscale Petrov-Galerkin method is employed for solution. On this basis, a matrix compression strategy is given, so that it is found that the a- mount of calculation can be greatly reduced. And it is proved that by using this method, the optimal con- vergent order of spectral approximation can be achieved by choosing appropriate truncation parameters.

关 键 词：特征值问题 多尺度Petrov-Galerkin法 弱奇异 

分 类 号：O178[理学—数学]