Fast and Rigorous Arbitrary-Precision Computation of Gauss--Legendre Quadrature Nodes and Weights

DOI10.1137/18M1170133OpenAlexW2963276001WikidataQ128853971 ScholiaQ128853971MaRDI QIDQ4560706

Fredrik Johansson, Marc Mezzarobba

Publication date: 7 December 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.03948

zbMATH Keywords

interval arithmeticGauss-Legendre quadratureLegendre polynomialsarbitrary-precision arithmetic

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Computer aspects of numerical algorithms (65Y99) Error analysis and interval analysis (65G99)

Related Items

Gauss-Legendre polynomial basis for the shape control of polynomial curves ⋮ Rounding error analysis of linear recurrences using generating series ⋮ Computation of Tight Enclosures for Laplacian Eigenvalues ⋮ Error bounds for the numerical evaluation of Legendre polynomials by a three-term recurrence ⋮ Fast and reliable high-accuracy computation of Gauss-Jacobi quadrature ⋮ Computing Hypergeometric Functions Rigorously ⋮ Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

Uses Software

• gmp
• PARI/GP
• DLMF
• ARPREC
• Arb

Cites Work

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