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On the computation of the Gauss–Legendre quadrature formula with a given precision

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
112
Identifiers
DOI: 10.1016/s0377-0427(99)00225-3
Keywords
  • Gaussian Quadrature
  • Legendre Polynomials
  • Newton Method
  • Root Finding

Abstract

Abstract The paper is concerned with error bounds for iterative methods for the numerical approximation of the zeros x ν of Legendre polynomials, i.e., the nodes of the Gauss–Legendre quadrature formula Q n G. From these bounds, new stopping criteria are derived. It is furthermore shown, how the calculation of the weights of Q n G may depend on the precision of the approximation of x ν .

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