An algorithm of incremental approximation of functions in a normed linear space by feedforward neural networks is presented. The concept of variation of a function with respect to a set is used to estimate the approxi...
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An algorithm of incremental approximation of functions in a normed linear space by feedforward neural networks is presented. The concept of variation of a function with respect to a set is used to estimate the approximation error together with the weight decay method, for optimizing the size and weights of a network in each iteration step of the algorithm. Two alternatives, recursively incremental and generally incremental, are proposed. In the generally incremental case, the algorithm optimizes parameters of all units in the hidden layer at each step. Tn the recursively incremental case, the algorithm optimizes the parameters corresponding to only one unit in the hidden layer at each step. In this case, an optimization problem with a smaller number of parameters is being solved at each step.
This paper deals with the continuity of the sharp constant K(T,X) with respect to the set T in the Jackson-Stechkin inequality E(f, L) <= K (T, X)omega(f, T, X), where E(f,L) is the best approximation of the functi...
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This paper deals with the continuity of the sharp constant K(T,X) with respect to the set T in the Jackson-Stechkin inequality E(f, L) <= K (T, X)omega(f, T, X), where E(f,L) is the best approximation of the function f a X by elements of the subspace L aS, X, and omega is a modulus of continuity, in the case where the space L (2)(, a",) is taken for X and the subspace of functions g a L (2)(, a",), for L. In particular, it is proved that the sharp constant in the Jackson-Stechkin inequality is continuous in the case where L is the space of trigonometric polynomials of nth order and the modulus of continuity omega is the classical modulus of continuity of rth order.
The technical constraints typical for the logical neuroblast model and the weaknesses of the widely applied artificial neural networks are specified. The composition method of the logical network of channel switches b...
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The technical constraints typical for the logical neuroblast model and the weaknesses of the widely applied artificial neural networks are specified. The composition method of the logical network of channel switches based on the approximation of the given function by individual fragments of its domain of definition is suggested. Integral criteria are introduced in order to ensure the algorithmic simplicity of the composition of the logical network for solving arbitrarily complex problems. Walsh spectral representations are used in the synthesis algorithm. The necessary explanations are accompanied by an example.
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