Recurrent evaluation of integrals of the type , with respect to numerical stability
Remarks on a Monte Carlo Integration Method.
Sharp bounds on the mathematical constant e.
Simple Monte Carlo integration with respect to Bernoulli convolutions
We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit...
Some double integral inequalities and applications.
Some Gauss-Type Formulae for the Evaluation of Cauchy Principal Values of Integrals.
Some generalized error inequalities and applications.
Some methods of numerical integration over a semi-infinite interval
Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type
MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...
Studies on the differential equations of enzyme kinetics. II: Bimolecular reaction: The fitting of experimental data to the simplified model.
Sur les quadratures.
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
The effect of reduced integration in the Steklov eigenvalue problem
In this paper we analyze the effect of introducing a numerical integration in the piecewise linear finite element approximation of the Steklov eigenvalue problem. We obtain optimal order error estimates for the eigenfunctions when this numerical integration is used and we prove that, for singular eigenfunctions, the eigenvalues obtained using this reduced integration are better approximations than those obtained using exact integration when the mesh size is small enough.
The estimates for the reminder term of some quadrature formulae.
The Numerical Evaluation of Cauchy Principal Values of Integrals by Romberg-Integration.
The Numerical Evaluation of Principal Value Integrals by Finite-Part Integration.
The Remainder Term in Quadrature Formulae.
Truncation Error Analysis by Means of Approximant Systems and Inclusion Regions.
Two sharp inequalities of Simpson type and applications.
Über optimale Quadraturformeln mit freien Knoten zu Hilberträumen periodischer Funktionen.