On the positivity of B-spline Wronskians

IF 1.4 2区数学 Q1 MATHEMATICS

Calcolo Pub Date : 2024-09-10 DOI:10.1007/s10092-024-00613-0

Michael S. Floater

引用次数: 0

Abstract

A proof that Wronskians of non-zero B-splines are positive is given, using only recursive formulas for B-splines and their derivatives. This could be used to generalize the de Boor–DeVore geometric proof of the Schoenberg–Whitney conditions and total positivity of B-splines to Hermite interpolation. For Wronskians of maximal order with respect to a given degree, positivity follows from a simple formula.

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关于 B-样条线 Wronskians 的实在性

仅使用 B-样条曲线及其导数的递推公式，就给出了非零 B-样条曲线的 Wronskians 为正的证明。这可用于将 Schoenberg-Whitney 条件的 de Boor-DeVore 几何证明和 B 样条曲线的全正性推广到 Hermite 插值。对于与给定阶数有关的最大阶的 Wronskians，正性由一个简单的公式得出。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Calcolo 数学-数学

CiteScore

2.40

自引率

11.80%

发文量

审稿时长

>12 weeks

期刊介绍： Calcolo is a quarterly of the Italian National Research Council, under the direction of the Institute for Informatics and Telematics in Pisa. Calcolo publishes original contributions in English on Numerical Analysis and its Applications, and on the Theory of Computation. The main focus of the journal is on Numerical Linear Algebra, Approximation Theory and its Applications, Numerical Solution of Differential and Integral Equations, Computational Complexity, Algorithmics, Mathematical Aspects of Computer Science, Optimization Theory. Expository papers will also appear from time to time as an introduction to emerging topics in one of the above mentioned fields. There will be a "Report" section, with abstracts of PhD Theses, news and reports from conferences and book reviews. All submissions will be carefully refereed.