تقرير
Moving Least Squares Approximation using Variably Scaled Discontinuous Weight Function
| العنوان: | Moving Least Squares Approximation using Variably Scaled Discontinuous Weight Function |
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| المؤلفون: | Esfahani, Mohammad Karimnejad, De Marchi, Stefano, Marchetti, Francesco |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | Functions with discontinuities appear in many applications such as image reconstruction, signal processing, optimal control problems, interface problems, engineering applications and so on. Accurate approximation and interpolation of these functions are therefore of great importance. In this paper, we design a moving least-squares approach for scattered data approximation that incorporates the discontinuities in the weight functions. The idea is to control the influence of the data sites on the approximant, not only with regards to their distance from the evaluation point, but also with respect to the discontinuity of the underlying function. We also provide an error estimate on a suitable {\it piecewise} Sobolev Space. The numerical experiments are in compliance with the convergence rate derived theoretically. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2302.02707 |
| رقم الأكسشن: | edsarx.2302.02707 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |