Calculation of Gauss-Kronrod quadrature rules

Source abstract

The Jacobi matrix of the ( 2 n + 1 ) (2n+1) -point Gauss-Kronrod quadrature rule for a given measure is calculated efficiently by a five-term recurrence relation. The algorithm uses only rational operations and is therefore also useful for obtaining the Jacobi-Kronrod matrix analytically. The nodes and weights can then be computed directly by standard software for Gaussian quadrature formulas.