Constructive Approximation

By Ronald A. DeVore, G. Lorentz. 1993

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Citations in the corpus

On the mathematical foundations of learning (2001, background): “(ii) The essence of Theorem 5, for the case n = 1, appears in [14].”
To understand deep learning we need to understand kernel learning (2018, methodology): “It can be shown [YRC07] that for kernel methods early stopping for gradient descent is effectively equivalent to traditional regularization methods, such as Tikhonov regularization.”
Adaptive piecewise polynomial estimation via trend filtering (2013, methodology): “1 of DeVore and Lorentz (1993)] when working with the usual definition of the Besov norms.”
Projection estimation in multiple regression with application to functional ANOVA models (1998, background): “Hence, the desired results follow from (8), (9), and the triangle inequality.”
Approximation of functions by a new class of generalized Bernstein–Schurer operators (2020, unknown): “Remark 1 There is an absolute constant > 0 such that (see [8]) −1ωβ 2 (h, √ δ) ≤ K2,β(z)(h, δ) ≤ ω 2 (h, √ δ).”
Adaptive estimation of the spectrum of a stationary Gaussian sequence (2001, background): “Indeed for f 2 B â, p,1, â. 1=p, we know from DeVore and Lorentz (1993) that k f ÿ f Pnk1 C(â)j f jâ, p Nÿ(âÿ1= p)n , where the de®nitions are quickly recalled below.”
Korovkin-type Theorems and Approximation by Positive Linear Operators (2010, unknown): “, to [8], [26], [38], [41], [42], [44], [45], [64], [65], [81-82], [83], [92], [109].”
Stochastic processes in random graphs (2004, unknown): “Since the function log(1 − t) is decreasing, by a Hardy–Littlewood inequality, see Bennett and Sharpley (1988) or DeVore and Lorentz (1993), ∫ 1 0 φ̇t log(1 − t) dt ≥ ∫ 1 0 φ̇ ∗ t log(1 − t) dt.”
Diffusion polynomial frames on metric measure spaces (2008, background): “Several characterizations of these spaces are given in [16].”
A data-driven block thresholding approach to wavelet estimation (2009, methodology): “Full details of Besov spaces are given, for example, in Triebel (1983) and DeVore and Lorentz (1993).”
CONSISTENCY OF RESTRICTED MAXIMUM LIKELIHOOD ESTIMATORS OF PRINCIPAL COMPONENTS (2008, background): “More details can be found in [7] and [8].”
Optimal sup-norm rates and uniform inference on nonlinear functionals of nonparametric IV regression (2015, background): “14See DeVore and Lorentz (1993) and Belloni et al. (2015) for examples of other bases with bounded Lebesgue constant or with Lebesgue constant diverging slowly with the sieve dimension.”