Cubature Error Bounds for Analytic Functions

Cubature Error Bounds for Analytic Functions

In this paper, two-dimensional cubature error bounds are developed. It is assumed that the function to be integrated is analytic, and that the domain of integration is contained in [—1, 1] X [—1, 1]. Tables of error constants for several cubature rules and domains of integration are included.

On the Smolyak cubature error for analytic functions

Error bounds for Gauss-Tur'an quadrature formulae of analytic functions

We study the kernels of the remainder term Rn,s(f) of GaussTurán quadrature formulas ∫ 1 −1 f(t)w(t) dt = n ∑

Sharp Error Bounds for Jacobi Expansions and Gegenbauer-Gauss Quadrature of Analytic Functions

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and val...

Error Bounds for Vector-valued Functions: Necessary

In this paper, we attempt to extend the definition and existing local error bound criteria to vector-valued functions, or more generally, to functions taking values in a normed linear space. Some new derivative-like objects (slopes and subdifferentials) are introduced and a general classification scheme of error bound criteria is presented.