| 小波阈值方法在Laplace方程中的应用 |
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| 引用本文： | 王伟芳,王晋茹.小波阈值方法在Laplace方程中的应用[J].唐山师范学院学报,2009,31(5):24-28. |
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| 作者姓名： | 王伟芳 王晋茹 |
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| 作者单位： | 北京工业大学,应用数理学院,北京,100124 |
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| 摘 要： | 把Laplace方程的柯西问题化为算子方程来考虑，右端项是非精确数据。运用小波对偶最小二乘法，得到了阶最佳的收敛性稳定性分析和非线性自适应。
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| 关 键 词： | Laplace方程 对偶最小二乘法 小波阈值 |
Application of Wavelet Shrinkage to Laplace Equation |
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| WANG Wei-fang,WANG Jin-ru.Application of Wavelet Shrinkage to Laplace Equation[J].Journal of Tangshan Teachers College,2009,31(5):24-28. |
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| Authors: | WANG Wei-fang WANG Jin-ru |
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| Institution: | (Department of Applied Mathematics, Beijing University ＆Technology, Beijing 100124, China) |
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| Abstract: | The Cauchy problem for the Laplace equation was considered in terms of the ill-posed operator eqation, with a given noisy right hand side. For a reconstruction of the solution from inaccurate data, the dual least squares method generated by the family of Shannon wavelet subspaces was applied. An explicit relation between the truncation level of the wavelet expansion was given, the convergence results including error estimate were obtained. According to the reference, the error estimate was order optimal. Next, a certain simple nonlinear modification of the method was investigated. |
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| Keywords: | Laplace equation dual least squares method wavelet shrinkage |
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