Self-validating integration and approximation of piecewise analytic functions
type: Item
instance of: scholarly article
title: Self-validating integration and approximation of piecewise analytic functions
zbMATH Open document ID: 1002.65030
DOI: 10.1016/S0377-0427(01)00586-6
author: Knut Petras
published in: Journal of Computational and Applied Mathematics
publication date: 2002-08-22T00:00:00Z
review text: Numerical quadrature rules are derived which are self-validating in the sense that interval arithmetic produce enclosures either for the integral or for the function itself. Under some circumstances these new quadrature rules can be shown to be optimal in the sense of operations count.
reviewed by: Thomas Sonar
Mathematics Subject Classification ID: 65D32
Mathematics Subject Classification ID: 65G20
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 1787694
zbMATH Keywords: piecewise analytic functions
zbMATH Keywords: enclosure techniques
zbMATH Keywords: result verification
zbMATH Keywords: numerical quadrature
zbMATH Keywords: interval arithmetic
describes a project that uses: QUADPACK
MaRDI profile type: Publication
cites work: Q5558293
cites work: Q3345690
cites work: Q4144703
cites work: Adaptive, Self-Validating Numerical Quadrature
cites work: Q3848301
cites work: Q5533688
cites work: Automatic, guaranteed integration of analytic functions
cites work: Q3999735
cites work: On the complexity of self-validating numerical integration and approximation of functions with singularities
cites work: Q4746719
cites work: Automatic differentiation: techniques and applications
description: scientific article; zbMATH DE number 1787694