Approximation by polynomials and ridge functions of classes of \(s\)-monotone radial functions

DOI10.1016/j.jat.2007.10.001zbMath1145.41005OpenAlexW2092384741MaRDI QIDQ927688

V. N. Konovalov, Dany Leviatan, Vitaly Maiorov

Publication date: 9 June 2008

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2007.10.001

zbMATH Keywords

polynomialsridge functionsradial functions\(s\)-monotone functions

Mathematics Subject Classification ID

Approximation by arbitrary nonlinear expressions; widths and entropy (41A46)

Related Items (9)

Approximation of Sobolev classes by polynomials and ridge functions ⋮ Meshless method with ridge basis functions ⋮ Essential rate for approximation by spherical neural networks ⋮ The ridge function representation of polynomials and an application to neural networks ⋮ Weighted moduli of smoothness of \(k\)-monotone functions and applications ⋮ Convex polynomial and ridge approximation of Lipschitz functions in \(\mathbb R^d\) ⋮ Some problems in the theory of ridge functions ⋮ The essential rate of approximation for radial function manifold ⋮ Deep neural networks for rotation-invariance approximation and learning

Cites Work

• Convex functions, partial orderings, and statistical applications
• Optimal reconstruction of a function from its projections
• On best approximation by ridge functions
• Widths and shape-preserving widths of Sobolev-type classes of \(s\)-monotone functions
• A criterion for \(n\)-convexity
• Freeknot splines approximation of Sobolev-type classes of \(s\)-monotone functions
• Best approximation by ridge functions in L p -spaces
• Orthogonal polynomials
• Approximation by Ridge Functions and Neural Networks
• Another Proof that Convex Functions are Locally Lipschitz
• Kolmogorov and linear widths of classes of s-monotone integrable functions
• 0n the best approximation by ridge functions in the uniform norm
• Kolmogorov and linear widths of weighted Sobolev-type classes on a finite interval. II
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