Explicit Gaussian quadrature rules for C1 cubic splines with symmetrically stretched knot sequences

Rachid Ait-Haddou; Michael Bartoň; Victor Manuel Calo

doi:10.1016/j.cam.2015.06.008

Explicit Gaussian quadrature rules for C¹ cubic splines with symmetrically stretched knot sequences

Rachid Ait-Haddou^*
, Michael Bartoň
, Victor Manuel Calo

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We provide explicit expressions for quadrature rules on the space of C¹ cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.

Original language	English
Pages (from-to)	543-552
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	290
DOIs	https://doi.org/10.1016/j.cam.2015.06.008
State	Published - 4 Jul 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

Keywords

B-splines
Cubic splines
Gaussian quadrature
Peano kernel

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.cam.2015.06.008

Cite this

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abstract = "We provide explicit expressions for quadrature rules on the space of C1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.",

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KW - B-splines

KW - Cubic splines

KW - Gaussian quadrature

KW - Peano kernel

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