A tchebycheffian extension of multidegree B-splines: Algorithmic computation and properties

René R. Hiemstra, Thomas J.R. Hughes, Carla Manni, Hendrik Speleers, Deepesh Toshniwal

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

In this paper, we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The extended Tchebycheff spaces and their dimensions are allowed to change from interval to interval. The approach works by constructing a matrix that maps a generalized Bernstein-like basis to the B-spline-like basis of interest. The B-spline-like basis shares many characterizing properties with classical univariate B-splines and may easily be incorporated in existing spline codes. This may contribute to the full exploitation of Tchebycheffian splines in applications, freeing them from the restricted role of an elegant theoretical extension of polynomial splines. Numerical examples are provided that illustrate the procedure described.

Original languageEnglish
Pages (from-to)1138-1163
Number of pages26
JournalSIAM Journal on Numerical Analysis
Volume58
Issue number2
DOIs
Publication statusPublished - 2020

Keywords

  • Extraction algorithms
  • Generalized B-splines
  • Multidegree B-splines
  • Tchebycheffian splines

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