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Simple Monte Carlo integration with respect to Bernoulli convolutions

David M. Gómez, Pablo Dartnell (2012)

Applications of Mathematics

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...

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

Milovanovic, Gradimir V., Cvetkovic, Aleksandar S. (2012)

Mathematica Balkanica New Series

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...

The effect of reduced integration in the Steklov eigenvalue problem

Maria G. Armentano (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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

María G. Armentano (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

Currently displaying 141 – 160 of 184