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<p>This paper investigates an extended interpolation process based on the zeros of Jacobi polynomials to approximate functions on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\([-1,1]^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mo stretchy="false">[</mo> <mo>-</mo> <mn>1</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. By combining a classical Lagrange interpolating polynomial sequence with its extended counterpart, a new mixed polynomial sequence is introduced, which significantly reduces the number of required function evaluations. Convergence conditions in suitable weighted function spaces are rigorously analyzed and some numerical tests are presented to support the efficiency of the proposed scheme.</p>

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Extended interpolation on the square and a mixed interpolating sequence

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月18日

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  • Ahmed Nasri,
  • Domenico Mezzanotte,
  • Donatella Occorsio

摘要

This paper investigates an extended interpolation process based on the zeros of Jacobi polynomials to approximate functions on \([-1,1]^2\) [ - 1 , 1 ] 2 . By combining a classical Lagrange interpolating polynomial sequence with its extended counterpart, a new mixed polynomial sequence is introduced, which significantly reduces the number of required function evaluations. Convergence conditions in suitable weighted function spaces are rigorously analyzed and some numerical tests are presented to support the efficiency of the proposed scheme.