The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on R is proved. Similar results have been recently obtained for the Jacobi weight on [−1, 1] and for the generalized Laguerre weight on [0,+∞). Numerical construction of the Gauss–Hermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few n...

It is shown how recent ideas on rational Gauss-type quadrature rules can be extended to Gauss-Kronrod, Gauss-Turr an, and Cauchy principal value quadrature rules. Numerical examples illustrate the advantages in accuracy thus achievable. 0. Introduction The idea of constructing quadrature rules that are exact for rational functions with prescribed poles, rather than for polynomials, has received...

This paper proposes a hybrid method to find cumulative distribution function (CDF) of completion time of GERT-type networks (GTN) which have no loop and have only exclusive-or nodes. Proposed method is cre-ated by combining an analytical transformation with Gaussian quadrature formula. Also the combined crude Monte Carlo simulation and combined conditional Monte Carlo simulation are developed a...

The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs and the beauty of these classical resul...

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...

Importance sampling (IS) and numerical integration methods are usually employed for approximating moments of complicated target distributions. In its basic procedure, the IS methodology randomly draws samples from a proposal distribution weights them accordingly, accounting mismatch between proposal. this work, we present general framework techniques inspired by methodology. The can also be see...

By a recent result on subperiodic trigonometric Gaussian quadrature, we construct a cubature formula of algebraic degree of exactness n on planar circular lenses (intersection of two overlapping disks) and “double bubbles” (union of two overlapping disks), with n2/2+O(n) nodes. An application is shown to RBF projection methods. 2000 AMS subject classification: 65D32.

A gaussian type quadrature formula, where the nodes are the zeros of Bessel functions of the first kind of order α (<(α) > −1), was recently proved for entire functions of exponential type. Here we relax the restriction on α as well as on the function. Some applications are also given.

After some remarks on the convergence order of the classical gaussian formula for the numerical evaluation of integrals on unbounded interval, the authors develop a new quadrature rule for the approximation of such integrals of interest in the practical applications. The convergence of the proposed algorithm is considered and some numerical examples are given.