The power of adaption for approximating functions with singularities

DOI10.1090/S0025-5718-08-02103-0zbMath1198.65262OpenAlexW1986143641MaRDI QIDQ3055072

Y. Zhao, Leszek Plaskota, Grzegorz W. Wasilkowski

Publication date: 7 November 2010

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-08-02103-0

zbMATH Keywords

samplingsingularitiesadaptive algorithmsfunction approximation

Mathematics Subject Classification ID

Numerical interpolation (65D05) Approximation by polynomials (41A10) Rate of convergence, degree of approximation (41A25) Complexity and performance of numerical algorithms (65Y20)

Related Items (16)

Local adaption for approximation and minimization of univariate functions ⋮ Efficient solution of IVPs with right-hand sides having discontinuities on an unknown hypersurface ⋮ Optimality of Euler-type algorithms for approximation of stochastic differential equations with discontinuous coefficients ⋮ Optimal solution of a class of non-autonomous initial-value problems with unknown singularities ⋮ Approximation of piecewise Hölder functions from inexact information ⋮ Monte Carlo integration of \(C^r\) functions with adaptive variance reduction: an asymptotic analysis ⋮ Complexity of the derivative-free solution of systems of IVPs with unknown singularity hypersurface ⋮ Solving systems of IVPs with discontinuous derivatives-numerical experiments ⋮ Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting ⋮ Optimal adaptive solution of initial-value problems with unknown singularities ⋮ The cost of deterministic, adaptive, automatic algorithms: cones, not balls ⋮ Optimal adaptive solution of piecewise regular systems of IVPs with unknown switching hypersurface ⋮ Minimal asymptotic error for one-point approximation of SDEs with time-irregular coefficients ⋮ Adaptive Itô-Taylor algorithm can optimally approximate the Itô integrals of singular functions ⋮ Automatic approximation using asymptotically optimal adaptive interpolation ⋮ Construction of nonlinear approximation schemes for piecewise smooth data

Uses Software

• QUADPACK
• CADRE
• Algorithm 145

Cites Work

• Deterministic and stochastic error bounds in numerical analysis
• Average-case analysis of numerical problems
• Information of varying cardinality
• On the power of adaption
• Adaption allows efficient integration of functions with unknown singularities
• On Skorokhod Convergence
• Optimal sequential and non-sequential procedures for evaluating a functional
• Ten Lectures on Wavelets
• A Metalgorithm for Adaptive Quadrature
• Noisy Information and Computational Complexity
• New tight frames of curvelets and optimal representations of objects with piecewise C² singularities
• Data compression and harmonic analysis
• Notes on the Adaptive Simpson Quadrature Routine
• Interpolation and Approximation of Piecewise Smooth Functions
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