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| 小波变换在求解第一类Fredholm积分方程中的应用 | |
| 引用本文： | 张海燕. 小波变换在求解第一类Fredholm积分方程中的应用[J]. 唐山学院学报, 2011, 24(3): 9-11 |
| 作者姓名： | 张海燕 |
| 作者单位： | 安徽科技学院理学院，安徽蚌埠,233100 |
| 基金项目： | 国家自然基金项目(50579061); 安徽科技学院引进人才项目(ZRC2009243) |
| 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。 |
| 关 键 词： | 小波变换 第一类Fredholm积分方程 反问题 正则化 |
Application of Wavelet Transform in Solving First Kind of Fredholm Integral Equation |
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| ZHANG Hai-yan. Application of Wavelet Transform in Solving First Kind of Fredholm Integral Equation[J]. Journal of Tangshan College, 2011, 24(3): 9-11 | |
| Authors: | ZHANG Hai-yan |
| Affiliation: | ZHANG Hai-yan(College of Science,Anhui Science and Technology University,Bengbu 233100,China) |
| Abstract: | 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 t... |
| Keywords: | wavelet transform the first kind of Fredholm integral equation inverse problem regularization |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |