Explicit Gaussian quadrature rules for C1 cubic splines with symmetrically stretched knot sequences
作者：
Highlights：
• The paper provides expressions for quadrature rules on the space of C1 cubic splines with non-uniform, symmetrically stretched knot sequences.
• Any function from the space is exactly integrated by the rule.
• The quadrature nodes and weights are derived via explicit recursion formulae, with no intervention of any numerical solver.
• The rule is optimal, i.e. it requires minimal number of nodes.
摘要
•The paper provides expressions for quadrature rules on the space of C1 cubic splines with non-uniform, symmetrically stretched knot sequences.•Any function from the space is exactly integrated by the rule.•The quadrature nodes and weights are derived via explicit recursion formulae, with no intervention of any numerical solver.•The rule is optimal, i.e. it requires minimal number of nodes.
论文关键词：Gaussian quadrature,Cubic splines,Peano kernel,B-splines
论文评审过程：Received 27 October 2014, Revised 12 February 2015, Available online 19 June 2015, Version of Record 1 July 2015.
论文官网地址：https://doi.org/10.1016/j.cam.2015.06.008
