The Gaussian integration of moments is systematically discussed. It is shown that the well-known diffusivityfactor approximation is equivalent to a one-node Gaussian quadrature. The limit as the moment power approaches infinity in a one-node Gaussian quadrature produces a diffusivity factor of e1/2 5 1.648 721 3, which is very close to the value of 1.66 suggested by Elsasser. The errors due to ...

An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...

The comparison of symbol error probability(SEP) for different M-ary modulation techniques over slow, flat, identically independently distributed Rician fading channel is presented in this paper. Because fading is one of the major limitations in wireless communication, so modulation technique with diversity is used to transmit message signal efficiently. Exact analysis of symbol error probabilit...

We present computational methods and subroutines to compute Gaussian quadrature integration formulas for arbitrary positive measures. For expensive integrands that can be factored into well-known forms, Gaussian quadrature schemes allow for efficient evaluation of high-accuracy and -precision numerical integrals, especially compared to general ad hoc schemes. In addition, for certain well-known...

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,...

We give a bivariate analog of the Micchelli-Rivlin quadrature for computing the integral of a function over the unit disk using its Radon projections. AMS subject classification: 65D32, 65D30, 41A55

Abstract. It was shown by P. J. Davis that the Newton-Cotes quadrature formula is convergent if the integrand is an analytic function that is regular in a sufficiently large region of the complex plane containing the interval of integration. In the present paper, a bound on the error of the Newton-Cotes quadrature formula for analytic functions is derived. Also the bounds on the Legendre polyno...

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.