Sampling, Marcinkiewicz–Zygmund inequalities, approximation, and quadrature rules

Inequalities between the Quadrature Operators and Error Bounds of Quadrature Rules

The order structure of the set of six operators connected with quadrature rules is established in the class of 3–convex functions. Convex combinations of these operators are studied and their error bounds for four times differentiable functions are given. In some cases they are obtained for less regular functions as in the classical results. Quadrature Rules, Inequalities and Error Bounds Szymo...

Quadrature Rules for Fuzzy Integrals

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-...

Approximation and Quadrature

Let V be a vector space with inner product (u, v) and norm u = (u, u) 1/2. We are given u ∈ V and a subspace˜V = span v (n) are linearly independent. We want to find p ∈ ˜ V such that u − p is minimal.

Information Theory and Quadrature Rules

Quadrature rules estimate ∫ 1 0 f(x) dx when f is defined by a table of n+1 values. Every binary string of length n defines a quadrature rule by choosing which endpoint of each interval represents the interval. The standard rules, such as Simpson’s Rule, correspond to strings of low Kolmogorov complexity, making it possible to define new quadrature rules with no smoothness assumptions, as well ...