Quadrature rules for $C^0$, $C^1$ splines, the real line, and the five (5) families

Helmut Ruhland

Quadrature rules for $C^0$, $C^1$ splines, the real line, and the five (5) families

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arxiv 1801.03388 v4 pith:OTCK6RYY submitted 2018-01-09 math.GM

Helmut Ruhland This is my paper · ORCID

classification math.GM

keywords rulesquadraturefamiliesfivelinerealallowcalculate

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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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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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