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Approximation properties of some two-layer feedforward neural networks

Nowak M. A.

Opuscula Mathematica

2007

Vol. 27, no. 1

59-72

In this article, we present a multiyariate two-layer feedforward neural networks that approximate continuos functions defined on [0, 1]d. We show that the L1 error of approximation is asymptotically proportional to the modulus of continuity of the underlying function taken at √d/n, where n is the number of function values used.

Approximation of functions of two variables by modified Szasz-Mirakyan operators

Walczak Z.

Fasciculi Mathematici

2001

Nr 31

117-128

We consider certain modified Szasz-Mirakyan operators in the exponential weighted spaces of continuous functions of two variables. We prove theorems on the degree of approximation, the Voronovskaya type theorem and we study some differential properties of these operators. The similar results for functions of one variable were given in [1] and [2].