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.
Quadrature rules for $C^0$, $C^1$ splines, the real line, and the five (5) families
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abstract
The five (5) families of quadrature rules with periods of one or two intervals for the real line and spline classes $C^0$, $C^1$ are presented. The formulae allow one to calculate the points or weights of these quadrature rules in a very simple manner as for the classical Gauss-Legendre rules.
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2019 1verdicts
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Quadrature rules for $C^0$ and $C^1$ splines, a recipe
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.