Principles of verified numerical integration

DOI10.1016/j.cam.2005.07.040zbMath1108.65016OpenAlexW2162811886MaRDI QIDQ861893

Knut Petras

Publication date: 2 February 2007

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

Full work available at URL: https://doi.org/10.1016/j.cam.2005.07.040

zbMATH Keywords

cubaturequadratureverified error boundsparameter-dependent integrands

Mathematics Subject Classification ID

Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Algorithms with automatic result verification (65G20)

Related Items (5)

Error estimates with explicit constants for sinc approximation, sinc quadrature and sinc indefinite integration ⋮ Some numerical integration methods based on Bernstein polynomials ⋮ A computer assisted proof of the symmetries of least energy nodal solutions on squares ⋮ 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
• filib++

Cites Work

• Automatic, guaranteed integration of analytic functions
• New methods for high-dimensional verified quadrature
• Gaussian quadrature formulae -- second Peano kernels, nodes, weights and Bessel functions
• Gaussian versus optimal integration of analytic functions
• Self-validating integration and approximation of piecewise analytic functions
• Smolyak cubature of given polynomial degree with few nodes for increasing dimension
• Gaussian integration of Chebyshev polynomials and analytic functions
• On the Smolyak cubature error for analytic functions
• High dimensional integration of smooth functions over cubes
• Adaptive, Self-Validating Numerical Quadrature
• ON THE ESTIMATION OF LINEAR FUNCTIONALS
• Numerical Software with Result Verification
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