{"title":"On the positivity of B-spline Wronskians","authors":"Michael S. Floater","doi":"10.1007/s10092-024-00613-0","DOIUrl":null,"url":null,"abstract":"<p>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.</p>","PeriodicalId":9522,"journal":{"name":"Calcolo","volume":"4 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calcolo","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10092-024-00613-0","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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