Characterization of the speed of convergence of the trapezoidal rule
type: Item
instance of: scholarly article
title: Characterization of the speed of convergence of the trapezoidal rule
zbMATH Open document ID: 0693.41031
DOI: 10.1007/BF01386402
author: Gerhard Schmeisser
author: Qazi I. Rahman
published in: Numerische Mathematik
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133440
review text: Our aim is to determine the precise space of functions for which the trapezoidal rule converges with a prescribed rate as the number of nodes tends to infinity. Excluding or controlling odd functions in some way it is possible to establish a correspondence between the speed of convergence and regularity properties of the function to be integrated. In this way we characterize Sobolev spaces, certain spaces of infinitely differentiable functions, of functions holomorphic in a strip, of entire functions of order greater than 1 and of entire functions of exponential type by the speed of convergence.
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 46E10
zbMATH DE Number: 4134740
zbMATH Keywords: trapezoidal rule
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: speed of convergence
MaRDI profile type: Publication
Wikidata QID: Q56339790
cites work: Q5338374
cites work: A two-dimensional mean problem
cites work: Q5833361
cites work: Umkehrsätze beim Trapezverfahren
cites work: Q5621638
cites work: Q3323133
cites work: Q3889125
cites work: The kernel of a rule of approximate integration
cites work: Q5599275
cites work: Characterization of Functions in Terms of Rate of Convergence of a Quadrature Process
cites work: Diophantine Approximations and Hilbert's Space
cites work: BEST QUADRATURE FORMULA FOR SOME CLASSES OF PERIODIC DIFFERENTIABLE FUNCTIONS
cites work: Best quadrature formula for the class \(W^rL_2\)
OpenAlex ID: W2079425628
Recommended article: The Exponentially Convergent Trapezoidal Rule
Recommended article: Rate of convergence in Trotter's approximation theorem
Recommended article: Rate of convergence in Trotter's approximation theorem and its applications
Recommended article: ON A STUDY OF ERROR BOUNDS OF TRAPEZOIDAL RULE
Recommended article: Towards a General Error Theory of the Trapezoidal Rule
Recommended article: Q4853991
Recommended article: On the convergence of the Trotter formula
Recommended article: Characterization of Functions in Terms of Rate of Convergence of a Quadrature Process
Recommended article: The trapezoidal rule for analytic functions of rapid decrease
Recommended article: Q5550288
description: scientific article; zbMATH DE number 4134740