Replacing points by compacta in neural network approximation |
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| Authors: | Paul C Kainen |
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| Institution: | Department of Mathematics, Georgetown University, Washington, DC 20057-1233, USA |
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| Abstract: | It is shown that cartesian product and pointwise-sum with a fixed compact set preserve various approximation-theoretic properties. Results for pointwise-sum are proved for F-spaces and so hold for any normed linear space, while the other results hold in general metric spaces. Applications are given to approximation of Lp-functions on the d-dimensional cube, 1?p<∞, by linear combinations of half-space characteristic functions; i.e., by Heaviside perceptron networks. |
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| Keywords: | primary 54E35 secondary 54B10 41A65 |
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