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arXiv · 1606.07940

On the representation by bivariate ridge functions

Rashid Aliev·Vugar Ismailov
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Abstract

We consider the problem of representation of a bivariate function by sums of ridge functions. We show that if a function of a certain smoothness class is represented by a sum of finitely many, arbitrarily behaved ridge functions, then it can also be represented by a sum of ridge functions of the same smoothness class. As an example, this result is applied to a homogeneous constant coefficient partial differential equation.

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Rashid Aliev, Vugar Ismailov. 2016-06-25. On the representation by bivariate ridge functions. https://arxiv.org/abs/1606.07940

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