On a smoothness problem in ridge function representation

DOI10.1016/j.aam.2015.11.002zbMath1342.26037OpenAlexW2192839088MaRDI QIDQ900985

Rashid A. Aliev, Vugar E. Ismailov

Publication date: 23 December 2015

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2015.11.002

zbMATH Keywords

smoothnessCauchy functional equationridge function

Mathematics Subject Classification ID

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

Related Items (8)

On some properties of finite sums of ridge functions defined on convex subsets of \(\mathbb{R}^n\) ⋮ A note on the equioscillation theorem for best ridge function approximation ⋮ Continuous sums of ridge functions on a convex body and the class VMO ⋮ On some properties of smooth sums of ridge functions ⋮ Some problems in the theory of ridge functions ⋮ 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

• Smoothness and uniqueness in ridge function representation
• On the continuity of finite sums of ridge functions
• Projection-based approximation and a duality with kernel methods
• Optimal reconstruction of a function from its projections
• Identifying linear combinations of ridge functions
• On best approximation by ridge functions
• Fundamentality of ridge functions
• On approximation by ridge functions
• Characterization of an extremal sum of ridge functions
• On Nonlinear Functions of Linear Combinations
• Approximation by ridge functions and neural networks with a bounded number of neurons
• Ridge Functions
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