Quasi orthogonal Jacobi polynomials and best one-sided image approximation to step functions

• Jorge Bustamante ^[1] ; Reinaldo Martínez-Cruz ^[1] ; José María Quesada ^[2]
  1. [1] Benemérita Universidad Autónoma de Puebla

     Benemérita Universidad Autónoma de Puebla

     México

     
  2. [2] Universidad de Jaén

     Universidad de Jaén

     Jaén, España

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 198, Nº 1 (October 2015), 2015, págs. 10-23
• Idioma: inglés
• DOI: 10.1016/j.jat.2015.05.001
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• Resumen

  • We find the polynomials of the best one-sided approximation to a step function on [−1,1]. We prove that these polynomials are obtained by Hermite interpolation at the zeros of some quasi orthogonal Jacobi polynomials. We discuss the cases when there is uniqueness and, if there is not, we determine the extremal points of the convex set of the best approximants.