Verified computed Peano constants and applications in numerical quadrature

DOI10.1007/s10543-007-0128-xzbMath1118.65007OpenAlexW2031106105MaRDI QIDQ996816

Chin-Yun Chen

Publication date: 19 July 2007

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-007-0128-x

zbMATH Keywords

error estimatesnumerical examplesinterval arithmeticbounded linear operatorerror functionalsquadrature errorPeano kernelsnumerical approximation of linear functionals

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Numerical solutions to equations with linear operators (65J10) Equations and inequalities involving linear operators, with vector unknowns (47A50) Algorithms for approximation of functions (65D15) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Bivariate product cubature using peano kernels for local error estimates, On the properties of Sard kernels and multiple error estimates for bounded linear functionals of bivariate functions with application to non-product cubature, Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities

Uses Software

• PASCAL-XSC

Cites Work

• On the definiteness of quadrature formulae of Clenshaw-Curtis type
• Automatic differentiation: techniques and applications
• Peano kernel behaviour and error bounds for symmetric quadrature formulas
• Computing interval enclosures for definite integrals by application of triple adaptive strategies
• ON THE ESTIMATION OF LINEAR FUNCTIONALS
• Cubature Error Bounds for Gauss-Legendre Product Rules
• The Geometry of Constrained Motion
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item