中文摘要：

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.

英文摘要：

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.