Voronovskaya type asymptotic expansions for multivariate quasi-interpolation neural network operators
نویسندگان
چکیده
منابع مشابه
Voronovskaya type asymptotic expansions for multivariate quasi-interpolation neural network operators
Here we study further the multivariate quasi-interpolation of sigmoidal and hyperbolic tangent types neural network operators of one hidden layer. We derive multivariate Voronovskaya type asymptotic expansions for the error of approximation of these operators to the unit operator. RESUMEN Aquí estudiamos extensiones de la cuasi-interpolación multivariada de operadores de redes neuronales de tip...
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‖u− Ihu‖L2(T ) ≤cThT ‖∇ku‖L2(ω̃T ), ‖u− Ihu‖L2(E) ≤cEh E ‖∇ku‖L2(ω̃E). Here, k ∈ {1, 2}, Ih is some quasi-interpolation operator, T and E are a simplex and a face thereof, hT and hE measure the size of T and E, and ω̃T and ω̃E are neighbourhoods of T and E which should be as small as possible. Note that the interpolate Ihu never needs to be computed explicitely. Moreover, for problems in two and th...
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ژورنال
عنوان ژورنال: Cubo (Temuco)
سال: 2014
ISSN: 0719-0646
DOI: 10.4067/s0719-06462014000200002