Journal Article10.1007/BF02252384
Algorithm 36 SNIFF: Efficient self-tuning algorithm for numerical integration
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TL;DR: A new adaptive algorithm for the integration of analytic functions is presented, obtained by choosing the 6-point Gauß-Legendre integration rule, which is provided with an accurate and very efficient integration process.
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Abstract: A new adaptive algorithm for the integration of analytic functions is presented. The algorithm processes the integration interval by generating local subintervals whose length is controlled through a feedback loop. Control is performed by means of a relation derived on an analytical basis and valid for an arbitrary integration rule: two different estimates of an integral are used to compute the interval length necessary to obtain an integral estimate with accuracy within the assigned error bounds. The implied method for local generation of subintervals and an effective assumption of error partition among subintervals give rise to an adaptive algorithm provided with an accurate and very efficient integration process.
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Citations
Adaptive Quadrature—Revisited
Walter Gander,Walter Gautschi +1 more
TL;DR: The basic principles of adaptive quadrature are reviewed and attention is drawn to serious deficiencies in the adaptive routines quad and quad8 provided by Matlab.
456
A review of error estimation in adaptive quadrature
TL;DR: A review of existing error estimation techniques and their differences and their common features can be found in this paper, where some common shortcomings of these algorithms are discussed, and a new general error estimation technique is presented.
60
Doubly Adaptive Quadrature Routines Based on Newton–Cotes Rules
TL;DR: This paper test two recently published Matlab codes, adaptsim and adaptlob, using both a Lyness–Kaganove test and a battery type of test and modify these two codes using sequences of null rules in the error estimator with the intention to increase the reliability for both codes.
Adaptive numerical integration in Element-Free Galerkin methods for elliptic boundary value problems
TL;DR: A method of distributing the integration points is devised which allows control over the integration accuracy for all elements of the stiffness matrix, while reducing the number of integration points required.
27
Adaptive through-thickness integration strategy for shell elements
I. Burchitz,T. Meinders,J. Huetink +2 more
- 25 May 2007
TL;DR: In this article, an adaptive through-thickness integration strategy for shell elements is developed, which consists of several algorithms that locate points of discontinuity in the out-of-plane stress profile, adapt sampling points, update values of internal variables, and perform numerical integration.
References
Cadre: an algorithm for numerical quadrature
Carl de Boor
- 01 Jan 1971
TL;DR: The CADRE algorithm as discussed by the authors uses the composite trapezoid sum to estimate the integral of F (x ) over suitably small subintervals of a given interval of integration, starting from the first such subinterval, the program attempts to find an acceptable estimate on a given sub-interval by cautious Romberg extrapolation.
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Algorithm 468: algorithm for automatic numerical integration over a finite interval [D1]
TL;DR: Submittal of an algorithm for consideration for publication in Communications of the A C M implies unrestricted use of the algorithm within a computer is permissible.
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