A New Analysis of Empirical Interpolation Methods and Chebyshev Greedy Algorithms
Copyright policy )A New Analysis of Empirical Interpolation Methods and Chebyshev Greedy Algorithms
We present new convergence estimates of generalized empirical interpolation methods in terms of the entropy numbers of the parametrized function class. Our analysis is transparent and leads to sharper convergence rates than the classical analysis via the Kolmogorov n-width. In addition, we also derive novel entropy-based convergence estimates of the Chebyshev greedy algorithm for sparse n-term nonlinear approximation of a target function. This also improves classical convergence analysis when corresponding entropy numbers decay fast enough.
18 pages, 4 figures
- Zhejiang Ocean University China (People's Republic of)
reduced basis greedy algorithm, 41A46, 41A65, 65J05, 65M12, Approximation by arbitrary nonlinear expressions; widths and entropy, Numerical Analysis (math.NA), General theory of numerical analysis in abstract spaces, metric entropy numbers, parametrized PDE, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), dictionary approximation, empirical interpolation method, Chebyshev greedy algorithm, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
reduced basis greedy algorithm, 41A46, 41A65, 65J05, 65M12, Approximation by arbitrary nonlinear expressions; widths and entropy, Numerical Analysis (math.NA), General theory of numerical analysis in abstract spaces, metric entropy numbers, parametrized PDE, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), dictionary approximation, empirical interpolation method, Chebyshev greedy algorithm, FOS: Mathematics, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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