Bivariate Product Cubature Using Peano Kernels for Local Error Estimates

Chen, Chin-Yun

doi:10.1007/s10915-007-9178-0

Cited by 3 publications

(2 citation statements)

References 9 publications

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“…As real numbers are identified to degenerated intervals, the interval arithmetic actually generalizes the real arithmetic, and mixed operations like 1 + [1, 2] = [2,3] are interpreted using (4).…”

Section: Interval Extensionsmentioning

confidence: 99%

“…Finally, the framework is instantiated with Taylor model based quadrature methods: Although other methods allow computing certified quadrature (e.g. [3][4][5]), Taylor models are efficient and have good asymptotical convergence properties. Experiments on standard benchmarks from the literature [6][7][8][9] are presented in Section 6 to support this convergence analysis.…”

Section: Introductionmentioning

confidence: 99%

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Convergence analysis and adaptive strategy for the certified quadrature over a set defined by inequalities

Goldsztejn

Cruz

Carvalho

2014

Journal of Computational and Applied Mathematics

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a b s t r a c tThis paper investigates the sufficient conditions for the asymptotic convergence of a generic branch and prune algorithm dedicated to the verified quadrature of a function in several variables. Quadrature over domains defined by inequalities, and adaptive meshing strategies are in the scope of this analysis. The framework is instantiated using certified quadrature methods based on Taylor models (i.e. Taylor approximations with rigorously bounded remainder), and reported experiments confirmed the analysis. They also show that the performances of the instantiated algorithm are comparable with current methods for certified quadrature.

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Section: Interval Extensionsmentioning

confidence: 99%