Approximation by superposition of sigmoidal and radial basis functions

Authors:
H.N Mhaskar;Charles A Micchelli
Affiliations:
Department of Mathematics, California State University, Los Angeles, California 90032 USA;IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598 USA
Venue:
Advances in Applied Mathematics
Year:
1992

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Abstract

Let @s: R - R be such that for some polynomial P, @sP is bounded. We consider the linear span of the functions {@s(@l . (x - t)): @l, t @e R^s}. We prove that unless @s is itself a polynomial, it is possible to uniformly approximate any continuous function on R^s arbitrarily well on every compact subset of R^s by functions in this span. Under more specific conditions on @s, we give algorithms to achieve this approximation and obtain Jackson-type theorems to estimate the degree of approximation.