Smoothness and uniqueness in ridge function representation

DOI10.1016/J.INDAG.2012.10.004zbMath1305.26036OpenAlexW2037484942MaRDI QIDQ740462

Allan Pinkus

Publication date: 3 September 2014

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2012.10.004

zbMATH Keywords

uniquenesssmoothnessCauchy functional equationridge function

Mathematics Subject Classification ID

Functional equations for real functions (39B22) Representation and superposition of functions (26B40)

Related Items (8)

Robust recovery of stream of pulses using convex optimization ⋮ Artificial neural network based response surface for data-driven dimensional analysis ⋮ A note on the equioscillation theorem for best ridge function approximation ⋮ On the continuity of finite sums of ridge functions ⋮ On a smoothness problem in ridge function representation ⋮ A note on continuous sums of ridge functions ⋮ On the representation by bivariate ridge functions ⋮ A representation problem for smooth sums of ridge functions

Cites Work

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• Sums of plane waves, and the range of the Radon transform
• Optimal reconstruction of a function from its projections
• Identifying linear combinations of ridge functions
• Fundamentality of ridge functions
• A General Functional Equation
• On Nonlinear Functions of Linear Combinations
• Consistency conditions for a finite set of projections of a function

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