Fractional Voronovskaya type asymptotic expansions for quasi-interpolation neural network operators

• George A Anastassiou ^[1]
  1. [1] University of Memphis

     University of Memphis

     Estados Unidos

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 14, Nº. 3, 2012, págs. 71-83
• Idioma: inglés
• DOI: 10.4067/S0719-06462012000300005
• Enlaces
  • Texto completo
• Resumen
  • español

    Estudiamos la cuasi-interpolación de los operadores de redes neuronales de tipo tangencial hiperbólico y sigmoidal de una capa oculta. Basados en la Teoría del Cálculo Fraccional, obtenemos expansiones asintóticas del tipo Voronovskaya para el error en la aproximación de estos operadores hacia el operador unitario.

  • English

    Here we study further the quasi-interpolation of sigmoidal and hyperbolic tangent types neural network operators of one hidden layer. Based on fractional calculus theory we derive fractional Voronovskaya type asymptotic expansions for the error of approximation of these operators to the unit operator.

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