APPROXIMATION BY SUPERPOSITION OF SIGMOIDAL AND RADIAL BASIS FUNCTIONS

被引：175

作者：

MHASKAR, HN ^{[1
]}

MICCHELLI, CA ^{[1
]}

机构：

[1] IBM CORP,THOMAS J WATSON RES CTR,YORKTOWN HTS,NY 10598

来源：

ADVANCES IN APPLIED MATHEMATICS | 1992年 / 13卷 / 03期

关键词：

D O I：

10.1016/0196-8858(92)90016-P

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let σ: R → R be such that for some polynomial P, σ P is bounded. We consider the linear span of the functions {σ(λ · (x - t)): λ, t ε{lunate} Rs}. We prove that unless σ is itself a polynomial, it is possible to uniformly approximate any continuous function on Rs arbitrarily well on every compact subset of Rs by functions in this span. Under more specific conditions on σ, we give algorithms to achieve this approximation and obtain Jackson-type theorems to estimate the degree of approximation. © 1992.

引用

页码：350 / 373

页数：24

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