Supporting vectors for the l1 norm and the l∞ norm and an application

  1. Sánchez-Alzola, Alberto
  2. García-Pacheco, Francisco Javier
  3. Naranjo-Guerra, Enrique
  4. Moreno-Pulido, Soledad
  1. 1 Department of Statistics and Operation Research, Collegeof Engineering, University of Cadiz, Puerto Real 11510,Spain
  2. 2 Universidad de Cádiz
    info

    Universidad de Cádiz

    Cádiz, España

    ROR https://ror.org/04mxxkb11

Revista:
Mathematical Sciences

ISSN: 2008-1359,  2251-7456

Año de publicación: 2021

Volumen: 15

Número: 2

Páginas: 173-187

Tipo: Artículo

DOI: 10.1007/S40096-021-00400-W GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: Mathematical Sciences

Resumen

A supporting vector of a matrix A for a certain norm II . II on Rn is a vector x such that II x II = 1 and II Ax II = II A II = max II y II = 1 II Ay II. In this manuscript, we characterize the existence of supporting vectors in the infinite-dimensional case for both the l1 -norm and the l∞ -norm. Besides this characterization, our theorems provide a description of the set of supporting vectors for operators on l∞ and l1. As an application of our results in the finite-dimensional case for both the l1 -norm and the l∞ -norm, we study meteorological data from stations located on the province of Cádiz (Spain). For it, we consider a matrix database with the highest temperature deviations of these stations.

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