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Hokkaido University Preprint Series in Mathematics >
Numerical differentiation of the second order derivative of functions with several variables
| Title: | Numerical differentiation of the second order derivative of functions with several variables |
| Authors: | Nakamura, Gen Browse this author | | Wang, Shengzhang Browse this author | | Wang, Yanbo Browse this author |
| Keywords: | Numerical di®erentiation | | Regularization | | Green function |
| Issue Date: | 2005 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 687 |
| Start Page: | 1 |
| End Page: | 26 |
| Abstract: | We propose a regularized optimization problem for computing numerical di®erentiation for the second order deriva- tive for functions with two variables from the noisy values of the function at scattered points, and give the proof of the existence and uniqueness of the solution of this problem. The reconstruc- tion scheme is also given during the proof, which is based on bi- harmonic Green function. The convergence estimate of the regular- ized solution to the exact solution for the regularized optimization problem as the regularized parameter and discrepancy of noisy data tending to zero is provided under a simple choice of regularization parameter. In the end we give the numerical examples and analyze the computational results. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69492 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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