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In this chapter we study the multivariate quantitative smooth approximation under differentiation of functions. The approximators here are multivariate neural network operators activated by the symmetrized and perturbed hyperbolic tangent activation function. All domains used here are infinite. The multivariate neural network operators are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give pointwise and uniform multivariate approximations with rates. We finish with illustrations.

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Symmetrized and Perturbed Hyperbolic Tangent Neural Network Multivariate Approximation over Infinite Domains

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  • 发表日期：

    2026年

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  • George A. Anastassiou

摘要

In this chapter we study the multivariate quantitative smooth approximation under differentiation of functions. The approximators here are multivariate neural network operators activated by the symmetrized and perturbed hyperbolic tangent activation function. All domains used here are infinite. The multivariate neural network operators are of quasi-interpolation type: the basic ones, the Kantorovich type ones, and of the quadrature type. We give pointwise and uniform multivariate approximations with rates. We finish with illustrations.