Some relationships are established between trigonometric quadrature and various classical quadrature formulas. In particular Gauss-Legendre quadrature is shown to be a limiting case of trigonometric quadrature. In an earlier paper [1] it was noted that there exist trigonometric and exponential analogs of Gaussian quadrature formulas. We now extend those results to show several interesting featu...

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi,...

By means of a fractional factorial simulation experiment, we compare the performance of Penalised Quasi-Likelihood, Non-Adaptive Gaussian Quadrature and Adaptive Gaussian Quadrature in estimating parameters for multi-level logistic regression models. The comparison is done in terms of bias, mean squared error, numerical convergence, and computational efficiency. It turns out that, in terms of M...

The use of Gaussian quadrature formulae is explored for the computation of the Macdonald function Kν(x) = ∫ ∞ 0 e cosh t cosh νt dt when x > 0 and ν is complex, ν = α+ iβ. It is shown that Gaussian quadrature with weight function w(t) = exp(−et) on [0,∞] is a viable approach, unless x is small and/or β large, but in combination with Gauss–Legendre quadrature, even in these latter cases.