Volume 45, pp. 371-404, 2016.
Gauss-Kronrod quadrature formulae - A survey of fifty years of research
Sotirios E. Notaris
Abstract
Kronrod in 1964, trying to estimate economically the error of the
Full Text (PDF) [440 KB], BibTeX
Key words
Gauss quadrature formula, Gauss-Kronrod quadrature formula, Stieltjes polynomials
AMS subject classifications
65D32, 33C45
Links to the cited ETNA articles
[2] | Vol. 9 (1999), pp. 26-38 G. S. Ammar, D. Calvetti, and L. Reichel: Computation of Gauss-Kronrod quadrature rules with non-positive weights |
[35] | Vol. 41 (2014), pp. 1-12 Aleksandar S. Cvetković and Miodrag M. Spalević: Estimating the error of Gauss-Turán quadrature formulas using their extensions |
[83] | Vol. 9 (1999), pp. 65-76 Walter Gautschi: Orthogonal polynomials and quadrature |
[87] | Vol. 25 (2006), pp. 129-137 Walter Gautschi: The circle theorem and related theorems for Gauss-type quadrature rules |
[129] | Vol. 28 (2007-2008), pp. 168-173 Dirk Laurie: Variable-precision arithmetic considered perilous - a detective story |
ETNA articles which cite this article
Vol. 45 (2016), pp. 405-419 D. Lj. Djukić, L. Reichel, M. M. Spalević, and J. D. Tomanović: Internality of generalized averaged Gauss rules and their truncations for Bernstein-Szegő weights |
Vol. 47 (2017), pp. 197-205 Nasim Eshghi, Lothar Reichel, and Miodrag M. Spalević: Enhanced matrix function approximation |
Vol. 50 (2018), pp. 20-35 Rada M. Mutavdžić, Aleksandar V. Pejčev, and Miodrag M. Spalević: Error bounds for Kronrod extension of generalizations of Micchelli-Rivlin quadrature formula for analytic functions |
Vol. 53 (2020), pp. 352-382 D. Lj. Djukić, R. M. Mutavdžić Djukić, A. V. Pejčev, and M. M. Spalević: Error estimates of Gaussian-type quadrature formulae for analytic functions on ellipses-a survey of recent results |
Vol. 59 (2023), pp. 145-156 Dusan Lj. Djukić, Rada M. Mutavdžić Djukić, Lothar Reichel, and Miodrag M. Spalević: Optimal averaged Padé-type approximants |
Vol. 59 (2023), pp. 230-249 Jelena Tomanović: Gauss-type quadrature rules with respect to external zeros of the integrand |
Vol. 61 (2024), pp. 92-104 Jelena Tomanović: Error estimates for Gauss-type quadrature rules for variable-sign weight functions |
Vol. 61 (2024), pp. 121-136 Carlos F. Borges and Lothar Reichel: Computation of Gauss-type quadrature rules |
Vol. 61 (2024), pp. 157-172 Dušan Lj. Djukić, Rada M. Mutavdžić Djukić, Aleksandar V. Pejčev, Lothar Reichel, Miodrag M. Spalević, and Stefan M. Spalević: Internality of two-measure-based generalized Gauss quadrature rules for modified Chebyshev measures |