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.

Hiemstra, R.r., Hughes, T., Manni, C., Speleers, H., Toshniwal, D. (2020). A Tchebycheffian extension of multidegree B-splines: algorithmic computation and properties. SIAM JOURNAL ON NUMERICAL ANALYSIS, 58(2), 1138-1163 [10.1137/19M1263583].

A Tchebycheffian extension of multidegree B-splines: algorithmic computation and properties

Manni, C;Speleers, H;
2020-04-13

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.
13-apr-2020
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/08 - ANALISI NUMERICA
English
Con Impact Factor ISI
Hiemstra, R.r., Hughes, T., Manni, C., Speleers, H., Toshniwal, D. (2020). A Tchebycheffian extension of multidegree B-splines: algorithmic computation and properties. SIAM JOURNAL ON NUMERICAL ANALYSIS, 58(2), 1138-1163 [10.1137/19M1263583].
Hiemstra, Rr; Hughes, Tjr; Manni, C; Speleers, H; Toshniwal, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/253372
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