|
This article is cited in 11 scientific papers (total in 11 papers)
Research Papers
Approximation by sums of ridge functions with fixed directions
V. E. Ismailov Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku, Azerbaijan
Abstract:
The paper contains a survey of some results about approximation of functions of several variables by sums of ridge functions with fixed directions. Also, some new theorems are proved, both for uniform approximation and for approximation in $L_2$
. These theorems generalize some results by the author known previously. The paper is finished by the study of the role of ridge functions in a problem of approximation by neural networks.
Keywords:
Ridge function, best approximation, superposition, cycle, path, neural network.
Received: 08.02.2015
Citation:
V. E. Ismailov, “Approximation by sums of ridge functions with fixed directions”, Algebra i Analiz, 28:6 (2016), 20–69; St. Petersburg Math. J., 28:6 (2017), 741–772
Linking options:
https://www.mathnet.ru/eng/aa1513 https://www.mathnet.ru/eng/aa/v28/i6/p20
|
Statistics & downloads: |
Abstract page: | 397 | Full-text PDF : | 100 | References: | 60 | First page: | 38 |
|