Constructing Approximations to Bivariate Piecewise-Smooth Functions
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914790800097280 |
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| author | Levin, David |
| author_facet | Levin, David |
| contents | This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a 3-corner. The given data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Constructing Approximations to Bivariate Piecewise-Smooth Functions Levin, David Numerical Analysis This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions with jump discontinuities or normal discontinuities across curves, and even across more involved geometries such as a 3-corner. The given data may be uniform or non-uniform, and noisy, and the approximation procedure involves non-linear least-squares minimization. Also included is a basic approximation theorem for functions with jump discontinuity across a smooth curve. |
| title | Constructing Approximations to Bivariate Piecewise-Smooth Functions |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2405.06462 |