Quadrature of hyperbola. [II.]

A Modified Monte - Carlo Quadrature . II

GPR Objects Hyperbola Region Feature Extraction

The shape and feature extraction in Ground Penetrating Radar (GPR) data is the most addressed application in present underground object identification technique. The problem of automatically detecting the shape and feature in GPR data is in analysing and fitting the hyperbola features from GPR data objects. To address these, we propose a hyperbole fitting method to extract the shape and feature...

Eberlein Measure and Mechanical Quadrature Formulae . II . Numerical Results

In a previous paper it was shown how a probability measure (Eberlein measure) on the closed unit ball of the sequence space, h, can be used to find the variance a2 of the error functional for a quadrature formula for the fc-dimensional cube, regarded as a random variable. Here we give values of a for some specific formulae.

Converse Quadrature Sum Inequalities for Freud Weights II

LetW := exp( Q), where Q is of smooth polynomial growth at1, for example Q(x) = jxj ; > 1. We call W 2 a Freud weight. Let fxjngnj=1 and f jngnj=1 denote respectively the zeros of the nth orthonormal polynomial pn for W 2 and the Christo¤el numbers of order n. We establish converse quadrature sum inequalities associated with W , such as k (PW ) (x) (1 + jxj) kLp(R) C n X j=1 jnW 2 (xjn) jPW j (...

Hierarchical quadrature for multidimensional singular integrals - Part II

In a previous part I, we introduced a method for the evaluation of singular integrals arising in the discretization of integral equations based on the repeated subdivision of domains. The integrals defined on these subdomains are classified such that a class of integrals can be expressed as a sum of regular integrals and representatives of other classes. A system of equations describes the rela...