On some aspects of approximation of ridge functions

2014/06/06 by Anton Kolleck, Kolleck, Anton, Jan Vybíral +1
Engineering · Mathematics · #41A25 #65D15 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.1406.1747

openalex publication_date 2014/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present effective algorithms for uniform approximation of multivariate functions satisfying some prescribed inner structure. We extend in several directions the analysis of recovery of ridge functions f(x)=g(⟨ a,x⟩) as performed earlier by one of the authors and his coauthors. We consider ridge functions defined on the unit cube [-1,1]d as well as recovery of ridge functions defined on the unit ball from noisy measurements. We conclude with the study of functions of the type f(x)=g(‖a-x‖l2d2).

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