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Exactness of quadrature formulas

Numerical Analysis 2021-01-26 v1 Numerical Analysis

Abstract

The standard design principle for quadrature formulas is that they should be exact for integrands of a given class, such as polynomials of a fixed degree. We show how this principle fails to predict the actual behavior in four cases: Newton-Cotes, Clenshaw-Curtis, Gauss-Legendre, and Gauss-Hermite quadrature. Three further examples are mentioned more briefly.

Keywords

Cite

@article{arxiv.2101.09501,
  title  = {Exactness of quadrature formulas},
  author = {Lloyd N. Trefethen},
  journal= {arXiv preprint arXiv:2101.09501},
  year   = {2021}
}