English

Generating nested quadrature formulas for general weight functions with known moments

Numerical Analysis 2016-04-22 v2 Numerical Analysis

Abstract

We revisit the problem of extending quadrature formulas for general weight functions, and provide a generalization of Patterson's method for the constant weight function. The method can be used to compute a nested sequence of quadrature formulas for integration with respect to any continuous probability measure on the real line with finite moments. The advantages of the method include that it works directly with the moments of the underlying distribution, and that for distributions with rational moments the existence of the formulas can be verified by exact rational arithmetic.

Keywords

Cite

@article{arxiv.1203.1554,
  title  = {Generating nested quadrature formulas for general weight functions with known moments},
  author = {Sanjay Mehrotra and Dávid Papp},
  journal= {arXiv preprint arXiv:1203.1554},
  year   = {2016}
}

Comments

Minor update in 2016: fixing a typo in the Mathematica code