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

Michael Barto\v{n}; Rachid Ait-Haddou; Victor Manuel Calo

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

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arxiv 1410.7196 v1 pith:IMV7FMUW submitted 2014-10-27 math.NA cs.NA

Rachid Ait-Haddou , Michael Bartoň , Victor Manuel Calo This is my paper · ORCID

classification math.NAcs.NA

keywords quadratureexplicitrulescubicknotnodesnon-uniformnumerical

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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 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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Quadrature rules for $C^0$ and $C^1$ splines, a recipe
math.NA 2019-08 conditional novelty 6.0 of 10

Closed formulas and a recursion produce Gaussian or one-parameter-optimal quadrature nodes and weights for C0 and C1 spline spaces on non-uniform, asymmetric partitions.

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