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Dirichlet principle using computers |
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| Authors: | Tsutomu Matsuura Saburou Saitoh § |
| Affiliation: | 1. Department of Mechanical Engineering , Faculty of Engineering, Gunma University , Kiryu 376-8515, Japan matsuura@me.gunma-u.ac.jp;3. Department of Mathematics , Faculty of Engineering, Gunma University , Kiryu 376-8515, Japan |
| Abstract: | In this article we shall give practical and numerical solutions of the Laplace equation on multidimensional spaces and show the numerical experiments by using computers. Our method is based on the Dirichlet principle by combinations with generalized inverses, Tikhonov's regularization and the theory of reproducing kernels. |
| Keywords: | Laplace equation Dirichlet problem Inverse problem Approximation of functions Reproducing kernel Tikhonov regularization Sobolev space Generalized inverse Approximate inverse AMS Subject Classifications: Primary 30C40 31A05 31B05 35J05 45B05 |