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.

Links to the cited ETNA articles

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