A wavelet-Galerkin method for high order numerical differentiation |
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| Authors: | Fang-Fang Dou Chu-Li Fu Yun-Jie Ma |
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| Institution: | a School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, PR China
b School of Applied Mathematics, University of Electronic and Science Technology of China, Chengdu 610054, PR China |
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| Abstract: | Numerical differentiation is a classical ill-posed problem. In this paper, we propose a wavelet-Galerkin method for high order numerical differentiation. By an appropriate choice of the regularization parameter an order optimal stability estimate of Hölder type is obtained. Some numerical examples show that the method is effective and stable. |
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| Keywords: | Numerical differentiation Ill-posed problem Wavelet-Galerkin method Regularization |
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