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Abstract <p>In this work, we consider the problem of constructing optimal interpolation formulas and we get such formulas that are exact to trigonometric functions <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8170_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="54" /> </InlineMediaObject> <EquationSource Format="TEX">\(\sin(\omega x)\)</EquationSource> <!--LobJMat2460813Hayotov-m1--> </InlineEquation> and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8170_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="56" /> </InlineMediaObject> <EquationSource Format="TEX">\(\cos(\omega x)\)</EquationSource> <!--LobJMat2460813Hayotov-m2--> </InlineEquation>, and algebraic polynomials of degree <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12202_2025_8170_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="58" /> </InlineMediaObject> <EquationSource Format="TEX">\((m-3)\)</EquationSource> <!--LobJMat2460813Hayotov-m3--> </InlineEquation> in the Hilbert space of differentiable functions. We obtain analytic formulas for the coefficients of the optimal interpolations formulas. In addition, we consider the problem of restoring curves given by parametric equations in the plane using optimal interpolation formulas.</p>

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Coefficients of Optimal Interpolation Formulas in the Hilbert Space of Differentiable Functions

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • A. R. Hayotov,
  • N. N. Doniyorov

摘要

Abstract

In this work, we consider the problem of constructing optimal interpolation formulas and we get such formulas that are exact to trigonometric functions \(\sin(\omega x)\) and \(\cos(\omega x)\) , and algebraic polynomials of degree \((m-3)\) in the Hilbert space of differentiable functions. We obtain analytic formulas for the coefficients of the optimal interpolations formulas. In addition, we consider the problem of restoring curves given by parametric equations in the plane using optimal interpolation formulas.