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<p>This paper provides interpolation and approximation techniques for continuous functions defined on an irregular grid within a box-domain of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2508_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {R}^{d}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>, using a new family of neural networks interpolation operators based on Lagrange polynomials. The approximation error is estimated by using higher order moduli of smoothness of the functions considered.</p>

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Higher Order Convergence of a Multivariate Neural Network Interpolation Operator for Irregular Grid

  • 期刊论文

  • 发表日期：

    2025年8月29日

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  • Danilo Costarelli,
  • Michele Piconi,
  • Manju Sharma,
  • Uaday Singh

摘要

This paper provides interpolation and approximation techniques for continuous functions defined on an irregular grid within a box-domain of \(\mathbb {R}^{d}\) R d , using a new family of neural networks interpolation operators based on Lagrange polynomials. The approximation error is estimated by using higher order moduli of smoothness of the functions considered.