تقرير
Interpolation by integrals on balls
| العنوان: | Interpolation by integrals on balls |
|---|---|
| المؤلفون: | Bruno, Ludovico Bruni, Elefante, Giacomo |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis |
| الوصف: | In this work we blend interpolation theory with numerical integration, constructing an interpolator based on integrals over $n$-dimensional balls. We show that, under hypotheses on the radius of the $n$-balls, the problem can be treated as an interpolation problem both on a collection of $(n-1)$-spheres $ S^{n-1} $ and multivariate point sets, for which a wide literature is available. With the aim of exact quadrature and cubature formulae, we offer a neat strategy for the exact computation of the Vandermonde matrix of the problem and propose a meaningful Lebesgue constant. Problematic situations are evidenced and a charming aspect is enlightened: the majority of the theoretical results only deal with the centre of the domains of integration and are not really sensitive to their radius. We flank our theoretical results by a large amount of comprehensive numerical examples. |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2312.10537Test |
| رقم الانضمام: | edsarx.2312.10537 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |