Self-validating integration and approximation of piecewise analytic functions

DOI10.1016/S0377-0427(01)00586-6zbMath1002.65030MaRDI QIDQ1612410

Knut Petras

Publication date: 22 August 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

numerical quadratureinterval arithmeticresult verificationpiecewise analytic functionsenclosure techniques

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Algorithms with automatic result verification (65G20)

Related Items (7)

Principles of verified numerical integration ⋮ Fast and Rigorous Arbitrary-Precision Computation of Gauss--Legendre Quadrature Nodes and Weights ⋮ Set-Membership Computation of Integrals with Uncertain Endpoints ⋮ Certified error bounds for uncertain elliptic equations ⋮ Computing Stieltjes constants using complex integration ⋮ On the Petras algorithm for verified integration of piecewise analytic functions ⋮ On the properties of Sard kernels and multiple error estimates for bounded linear functionals of bivariate functions with application to non-product cubature

Uses Software

• QUADPACK

Cites Work

• Automatic differentiation: techniques and applications
• Automatic, guaranteed integration of analytic functions
• On the complexity of self-validating numerical integration and approximation of functions with singularities
• Adaptive, Self-Validating Numerical Quadrature
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