Journal article
Finding Optimal Weight Vectors for Ridge Function Approximation in L2 (D)*
SIAM journal on optimization, Vol.35(3), pp.1655-1672
09/30/2025
DOI: 10.1137/24M166632X
Abstract
Ridge functions on a set D \subset Rn are mappings D-* R of the form x H-* \varphi(wTx) for given w \in Rn and function \varphi: R-* R. We assume that D is compact with nonempty interior and Lipschitz boundary. Given W = {w1, w2,..., wm}, let V\scrW be the set of all functions of the form x H-\sumjm=1 \varphij(wjT x) where \varphij \in C(R), the set of continuous functions R-* R. Clearly V\scrW is a subspace of L2(D). The task in this paper is, given D, to characterize and find a set W \subset Rn of m weight vectors that minimizes (W) := maxf:|f|H1(D)\leq1 infg\inV\scrW f * gL2(D). The maximizing f is shown to exist and can be interpreted as the function ``hardest to approximate"" by V\scrW. The value of (W) is given in terms of the maximum eigenvalue of a self-adjoint compact operator L2(D)-* L2(D). Computational methods are given for both computing (W), given W, and finding W that approximately minimizes (W) through a gradient descent procedure.
Details
- Title: Subtitle
- Finding Optimal Weight Vectors for Ridge Function Approximation in L2 (D)*
- Creators
- David E. Stewart - University of Iowa
- Resource Type
- Journal article
- Publication Details
- SIAM journal on optimization, Vol.35(3), pp.1655-1672
- DOI
- 10.1137/24M166632X
- ISSN
- 1052-6234
- eISSN
- 1095-7189
- Publisher
- SIAM PUBLICATIONS; PHILADELPHIA
- Language
- English
- Date published
- 09/30/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984927079502771
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