Gaussian quadrature rules for C¹ quintic splines

2015/03/03 by Michael Bartoň, Bartoň, Michael, Rachid Ait-Haddou +3
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #FOS: Mathematics #Image and Object Detection Techniques #Numerical Analysis (math.NA) #Tribology and Lubrication Engineering

paper · pdf · doi:10.48550/arxiv.1503.00907

openalex publication_date 2015/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We provide explicit expressions for quadrature rules on the space of C¹ quintic splines with uniform knot sequences over finite domains. 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 the minimal number of nodes. For each of n subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/3 when compared to the classical Gaussian quadrature for polynomials. Numerical experiments show fast convergence, as n grows, to the "two-third" quadrature rule of Hughes et al. for infinite domains.

Citations

• On calculating with B-splines

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