On the representation by bivariate ridge functions | Zendy

Rashid A. Aliev | Zendy; Aysel A. Asgarova | Zendy; Vugar E. Ismailov | Zendy

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On the representation by bivariate ridge functions

Author(s) -

Rashid A. Aliev,

Aysel A. Asgarova,

Vugar E. Ismailov

Publication year - 2021

Publication title -

ukrains’kyi matematychnyi zhurnal

Language(s) - English

Resource type - Journals

ISSN - 1027-3190

DOI - 10.37863/umzh.v73i5.263

Subject(s) - smoothness , bivariate analysis , ridge , mathematics , function (biology) , class (philosophy) , representation (politics) , mathematical analysis , pure mathematics , constant (computer programming) , partial differential equation , homogeneous , combinatorics , statistics , computer science , geology , paleontology , evolutionary biology , artificial intelligence , politics , political science , law , biology , programming language

UDC 517.5We consider the problem of representation of a bivariate function by sums of ridge functions. It is shown 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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