تقرير
Polynomial Interpolation of Function Averages on Interval Segments
| العنوان: | Polynomial Interpolation of Function Averages on Interval Segments |
|---|---|
| المؤلفون: | Bruno, Ludovico Bruni, Erb, Wolfgang |
| سنة النشر: | 2023 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 41A05, 41A10, 41A25, 65D05 |
| الوصف: | Motivated by polynomial approximations of differential forms, we study analytical and numerical properties of a polynomial interpolation problem that relies on function averages over interval segments. The usage of segment data gives rise to new theoretical and practical aspects that distinguish this problem considerably from classical nodal interpolation. We will analyse fundamental mathematical properties of this problem as existence, uniqueness and numerical conditioning of its solution. We will provide concrete conditions for unisolvence, explicit Lagrange-type basis systems for its representation, and a numerical method for its solution. To study the numerical conditioning, we will provide concrete bounds of the Lebesgue constant in a few distinguished cases. Comment: 20 pages, 5 figures |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.00328 |
| رقم الأكسشن: | edsarx.2309.00328 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |