带小波函数的Cauchy主值积分的数值计算

1 引言 众所周知,小波方法在信号处理和图像处理方面发挥了举世瞩目的成就。近年来人们研究小波方法在数值分析方面的应用。期望在数值求解微分方程和积分方程方面发挥良好的作用。本文研究带有小波函数的Cauchy主值积分 的数值计算方法,其中Φ(x)是紧支撑的尺度函数。这是数值求解积分方程的核心问题之一。 1.l 多分辩分析 空间L~2(R)中的一个多分辩分析是这样的闭子空间列{V_j},它满足下列条件 1) 2) 3) 4)存在尺度函数,使构成V_o的Riesz基,从而也存在序列使满足双尺度方程

CALCULATION FOR CAUCHY PRINCIPLE INTEGRAL WITH SCALING FUNCTIONS

In this paper a numerical method to calculate one-dimensional Cauchy principle value integrals with scaling functions is presented. It's an essential problem that arise when using wavelets to discrete the singular integral equation of Cauchy type. At first, multiresolution analysis and wavelets is recalled. Meanwhile, the dif-ficulties to deal with this problem are discussed in brief. Then we take the advan-tages of the relations between wavelets and orthogonal polynomials to cope with the problem. At the end the numerical results are given.