Accuracy of approximations of solutions to Fredholm equations by kernel methods

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• 作者：Giorgio Gnecco^a ; ^{giorgio.gnecco@dist.unige.it} ; V臎ra K暖rková ; ^b ; ^{vera@cs.cas.cz} ; Marcello Sanguineti^a ; ^{marcello@dist.unige.it}
• 关键词：Approximate solutions to integral equations ; Radial and kernel-based networks ; Gaussian kernels ; Model complexity ; Analysis of algorithms
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：15 March, 2012
• 卷：218
• 期：14
• 页码：7481-7497
• 文件大小：341 K

摘要

Approximate solutions to inhomogeneous Fredholm integral equations of the second kind by radial and kernel networks are investigated. Upper bounds are derived on errors in approximation of solutions of these equations by networks with increasing model complexity. The bounds are obtained using results from nonlinear approximation theory. The results are applied to networks with Gaussian and kernel units and illustrated by numerical simulations.