用矩阵近似分解方法求解第二类积分方程

Fast Algorithm for Second Kind Integral Equations by Matrix Approximative Decomposition

基于区域分解和多项式插值，对积分算子进行离散，得到高精确度的近似离散矩阵．这一方法适应于核函数为光滑、振动较小、只有有限弱奇点的情形．如果采用ｎ个离散点，近似矩阵可以经过Ｏ（ｎ）次计算得到，存储也只要Ｏ（ｎ）．矩阵－向量相乘的计算量为Ｏ（ｎｌｏｇｎ）．所以。

Based on polynomial interpolation, we present a fast algorithm to approximate matrices arising from the discretization of second kind integral equations where the kernel function is either smooth, non oscillatory and possessing only a finite number of singularities. The approximation can be constructed in O(n) operations and requires O(n) storage, where n is the number of quadrature points used in the discretization. Moreover, the matrix vector multiplication cost is of order O(n log n). Thus our scheme is well suitable for conjugate gradient type methods.