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This paper deals with the estimation of the quadrature error of a Gaussian formula for weight functions involving powers, exponentials and Bessel functions of the first kind. For this purpose, in this work the averaged and generalized ...

• Useful a posteriori error approximations for a Gaussian rule.
• Heuristic a ...

In this paper, an adaptive element Subdivision Method based on the Affine transformations and Partitioning techniques (APSM) is presented for evaluating the weakly singular integrals with arbitrary shape of elements. The basic idea ...

Gaussian quadrature rules are a classical tool for the numerical approximation of integrals with smooth integrands and positive weight functions. We derive and explicitly list asymptotic expressions for the points and weights of Gaussian ...

• Gaussian quadrature rules can be computed efficiently from asymptotic expansions.
• Generalized weight functions include all classical orthogonal polynomials as special cases.
• Extensions of Riemann-Hilbert analyses are validated.

In this work we develop the Gaussian quadrature rule for weight functions involving powers, exponentials and Bessel functions of the first kind. Besides the computation based on the use of the standard and the modified Chebyshev algorithm, here we ...

Although Hermite functions have been studied for over a century and have been useful for analytical and numerical solutions in a myriad of areas, the theory of Hermite functions has gaps. This article is a unified treatment of all the ...

The Clausen functions arise in numerous applications. An efficient summation/integration method for the numerical calculation of these functions of arbitrary order is proposed in this paper. The method is based on a modification of an earlier ...

We consider the computation of quadrature rules that are exact for a Chebyshev set of linearly independent functions on an interval $[a,b]$. A general theory of Chebyshev sets guarantees the existence of rules with a Gaussian property, in the sense that $...

Iterative methods with certified convergence for the computation of Gauss–Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be generally ...

Although using non-Gaussian distributions in economic models has become increasingly popular, currently there is no systematic way for calibrating a discrete distribution from the data without imposing parametric assumptions. This paper proposes a ...

A general-purpose C++ software program called CGPOPS is described for solving multiple-phase optimal control problems using adaptive direct orthogonal collocation methods. The software employs a Legendre-Gauss-Radau direct orthogonal collocation method ...

• Numerical integration of polygonal finite elements is not well-established.
• Two ...

This paper aims to determine which numerical integration method shows the best performance when integrating the polygonal finite element stiffness matrix. Hence, numerical comparisons were made between two existing methods, ...

We study worst-case optimal approximation of positive linear functionals in reproducing kernel Hilbert spaces induced by increasingly flat Gaussian kernels. This provides a new perspective and some generalisations to the problem of interpolation ...

We explore the computational issues concerning a new algorithm for the classical least-squares approximation of $N$ samples by an algebraic polynomial of degree at most $n$ when the number $N$ of the samples is very large. The algorithm is based on a ...

An adaptive and efficient volume element subdivision method using binary tree for evaluation of nearly singular domain integrals with continuous or discontinuous kernel in three-dimensional (3-D) boundary element method (BEM) has been ...

• The BTSM is proposed for evaluating nearly singular integrals with various kernel.

In this article, numerical integration is formulated as evaluation of a matrix function of a matrix that is obtained as a projection of the multiplication operator on a finite-dimensional basis. The idea is to approximate the ...

The objective of the paper is that of constructing finite Gaussian mixture approximations to analytically intractable density kernels. The proposed method is adaptive in that terms are added one at the time and the mixture is fully re-optimized at each ...

The value of a highly oscillatory integral is typically determined asymptotically by the behavior of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary points or saddle ...

Many of the input-parameter-to-output-quantity-of-interest maps that arise in computational science admit a surprising low-dimensional structure, where the outputs vary primarily along a handful of directions in the high-dimensional input space. This type ...

Likelihood-based estimation of the normal-gamma stochastic frontier model requires numerical integration to solve its likelihood. For the integration methods found in the literature, it is not known under which conditions they perform optimally or if ...

We solve the first order 2-D reaction–diffusion equations which describe binding-diffusion kinetics using the photobleaching scanning profile of a confocal laser scanning microscope, approximated by a Gaussian laser profile. We show ...