Symmetric triangle quadrature rules for arbitrary functions

Quadrature rules for rational functions

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...

Quadrature Rules for Fuzzy Integrals

Gauss-type Quadrature Rules for Rational Functions

When integrating functions that have poles outside the interval of integration, but are regular otherwise, it is suggested that the quadrature rule in question ought to integrate exactly not only polynomials (if any), but also suitable rational functions. The latter are to be chosen so as to match the most important poles of the integrand. We describe two methods for generating such quadrature ...

Approximate Inclusion - Exclusion for Arbitrary Symmetric Functions ∗

Let A 1 , A 2 ,. .. , A n be events in some probability space. The approximate inclusion-exclusion problem, due to Linial and Nisan (1990), is to estimate Pr[A 1 ∪· · ·∪A n ] given Pr[ i∈S A i ] for all |S | k. Kahn et al. (1996) solve this problem optimally for each k. We study the following more general question: given Pr[ i∈S A i ] for all |S | k, estimate Pr the number of events among A 1 ,...

Symmetric Gauss Legendre Quadrature Rules for Numerical Integration over an Arbitrary Linear Tetrahedra in Euclidean Three-Dimensional Space

In this paper it is proposed to compute the volume integral of certain functions whose antiderivates with respect to one of the variates (say either x or y or z) is available. Then by use of the well known Gauss Divergence theorem, it can be shown that the volume integral of such a function is expressible as sum of four integrals over the unit triangle. The present method can also evaluate the ...