relation: http://eprints.imtlucca.it/1719/
title: On a Variational Norm Tailored to Variable-Basis Approximation Schemes
creator: Gnecco, Giorgio
creator: Sanguineti, Marcello
subject: QA75 Electronic computers. Computer science
description: A variational norm associated with sets of computational units and used in function approximation, learning from data, and infinite-dimensional optimization is investigated. For sets Gk obtained by varying a vector y of parameters in a fixed-structure computational unit K(-,y) (e.g., the set of Gaussians with free centers and widths), upper and lower bounds on the GK -variation norms of functions having certain integral representations are given, in terms of the £1-norms of the weighting functions in such representations. Families of functions for which the two norms are equal are described.
publisher: IEEE
date: 2011
type: Article
type: PeerReviewed
identifier:   Gnecco, Giorgio and Sanguineti, Marcello  On a Variational Norm Tailored to Variable-Basis Approximation Schemes.  IEEE Transactions on Information Theory, 57 (1).  pp. 549-558.  ISSN 0018-9448      (2011)  
relation: http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5673958&isnumber=5673678
relation: 10.1109/TIT.2010.2090198