中文摘要：

提出将第一类Fredholm积分方程离散为线性不适定方程,并利用小波变换方法进行数值求解。该方法将小波变换与正则化方法、Schur补共轭梯度法相结合,选取小波函数作为一组基底,将原不适定问题转化为粗子空间上的适定问题。通过数值实验验证了该方法的有效性和可行性。

英文摘要：

The first kind of Fredholm integral equation is dispersed to be a linear ill-posed one.A method of wavelet transform is presented for the solution of the linear ill-posed problem.The equation combines wavelet transform with regularization method and Schur CG algorithm to solve ill-posed problems,and chooses a wavelet function as the base function,which takes full advantage of the wavelet with compact support,and converts the ill-posed problem into a posed one in the coarse space.The numerical results show the applicability and effectiveness of the proposed method.