Volume 9, pp. 26-38, 1999.

Computation of Gauss-Kronrod quadrature rules with non-positive weights

G. S. Ammar, D. Calvetti, and L. Reichel

Abstract

Recently Laurie presented a fast algorithm for the computation of $(2n+1)$-point Gauss-Kronrod quadrature rules with real nodes and positive weights. We describe modifications of this algorithm that allow the computation of Gauss-Kronrod quadrature rules with complex conjugate nodes and weights or with real nodes and positive and negative weights.

Full Text (PDF) [106 KB]

Key words

orthogonal polynomials, indefinite measure, fast algorithm, inverse eigenvalue problem.

AMS subject classifications

Links to the cited ETNA articles

[8]Vol. 9 (1999), pp. 65-76 Walter Gautschi: Orthogonal polynomials and quadrature

ETNA articles which cite this article

Vol. 45 (2016), pp. 371-404 Sotirios E. Notaris: Gauss-Kronrod quadrature formulae - A survey of fifty years of research
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

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