Reliability Conditions in Quadrature Algorithms
Gh. Adam, S. Adam, and N.M. Plakida
TL;DR
This paper presents a method to assess the reliability of quadrature algorithms by analyzing the integrand's profile at quadrature knots, improving success rates especially for complex parametric integrals.
Contribution
It introduces a novel analysis technique for integrand profiles at quadrature points to enhance reliability assessment in numerical integration.
Findings
Approach approaches 100% success rate in ideal conditions
Effective for complex parametric integrals
Improves reliability of quadrature outputs
Abstract
The detection of insufficiently resolved or ill-conditioned integrand structures is critical for the reliability assessment of the quadrature rule outputs. We discuss a method of analysis of the profile of the integrand at the quadrature knots which allows inferences approaching the theoretical 100% rate of success, under error estimate sharpening. The proposed procedure is of the highest interest for the solution of parametric integrals arising in complex physical models.
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Taxonomy
TopicsControl Systems and Identification