The nature of the nodes, weights and degree of precision in Gaussian quadrature rules

• Autores: J.S.C. Prentice
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 42, Nº. 1, 2011, págs. 109-117
• Idioma: inglés
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• Resumen

  • We present a comprehensive proof of the theorem that relates the weights and nodes of a Gaussian quadrature rule to its degree of precision. This level of detail is often absent in modern texts on numerical analysis. We show that the degree of precision is maximal, and that the approximation error in Gaussian quadrature is minimal, in a least-squares sense.