A constraint on extensible quadrature rules

A constraint on extensible quadrature rules

When the worst case integration error in a family of functions decays as n−α for some α > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 < · · · < ∞, then these sample sizes must grow at least geometrically. More precisely, nk+1/nk ≥ ρmust hold for a value 1 < ρ < 2 that increases with α. This result always rules out arithmetic sequences but ...

A CONSTRAINT ON EXTENSIBLE QUADRATURE RULES By Art

When the worst case integration error in a family of functions decays as n−α for some α > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 < · · · < ∞, then these sample sizes must grow at least geometrically. More precisely, nk+1/nk ≥ ρmust hold for a value 1 < ρ < 2 that increases with α. This result always rules out arithmetic sequences but ...

Quadrature Rules for Fuzzy Integrals

Quadrature rules on unbounded interval

After some remarks on the convergence order of the classical gaussian formula for the numerical evaluation of integrals on unbounded interval, the authors develop a new quadrature rule for the approximation of such integrals of interest in the practical applications. The convergence of the proposed algorithm is considered and some numerical examples are given.

Weighted quadrature rules with binomial nodes

In this paper, a new class of a weighted quadrature rule is represented as --------------------------------------------  where  is a weight function,  are interpolation nodes,  are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as   that  and we obtain the explicit expressions of the coefficients  using the q-...