New methods for high-dimensional verified quadrature

DOI10.1023/A:1026437523641zbMath0947.65026OpenAlexW2115900448MaRDI QIDQ1300081

Kyoko Makino, Martin Berz

Publication date: 2 November 2000

Published in: Reliable Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1026437523641

zbMATH Keywords

cubaturenumerical examplesnumerical quadratureinterval arithmeticTaylor polynomialmulti-dimensionverified intervalverified quadrature

Mathematics Subject Classification ID

Interval and finite arithmetic (65G30) Multidimensional problems (41A63) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32) Algorithms with automatic result verification (65G20)

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Recent advances in a rigorous computation of Poincaré maps ⋮ Principles of verified numerical integration ⋮ Interval uncertain method for multibody mechanical systems using Chebyshev inclusion functions ⋮ Status of the differential transformation method ⋮ Remarks on geometric properties of SQG sharp fronts and \(\alpha\)-patches ⋮ Nogood-based asynchronous forward checking algorithms ⋮ An implicit algorithm for validated enclosures of the solutions to variational equations for ODEs ⋮ Global Smooth Solutions for the Inviscid SQG Equation ⋮ On the properties of Sard kernels and multiple error estimates for bounded linear functionals of bivariate functions with application to non-product cubature ⋮ Taylor models and floating-point arithmetic: proof that arithmetic operations are validated in COSY ⋮ Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities ⋮ CAPD::DynSys: a flexible C++ toolbox for rigorous numerical analysis of dynamical systems ⋮ Computer-assisted proofs in PDE: a survey

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