Publications

Explicit Gaussian quadrature rules for cubic splines with non-uniform knot sequences

Bibliography:

R. Ait-Haddou, M. Barton, Victor Manuel V. Calo, "Explicit Gaussian quadrature rules for cubic splines with non-uniform knot sequences", Journal of Computational and Applied Mathematics, submitted, 2014.

Authors:

R. Ait-Haddou, M. Barton, V. Calo

Keywords:

Gaussian quadrature, cubic splines, Peano kernel, B-splines

Year:

2014

Abstract:

We provide explicit expressions for quadrature rules
on the space of $C^1$ cubic splines with non-uniform, symmetrically stretched knot sequences.
The quadrature nodes and weights are derived via an explicit recursion
that avoids \cre{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.

ISSN:

1