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Model of Lagrange Two-dimensional Interpolation Based on Dimensionality Reduction.

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Title: Model of Lagrange Two-dimensional Interpolation Based on Dimensionality Reduction.
Authors: Zhihua Feng1,2 fzh@djtu.edu.cn, Dayong Zhou3 zhoudy102@163.com
Source: IAENG International Journal of Applied Mathematics. Jul2025, Vol. 55 Issue 7, p2330-2335. 6p.
Subjects: Numerical functions, Interpolation, Mathematical models, Two-dimensional models, Polynomials
Abstract: Data interpolation is a common challenge in both scientific research and engineering. Multidimensional interpolation, which encompasses one-dimensional interpolation as a subset, covers a broader range of problems. Notably, interpolation issues in dimensions higher than three can be reduced to a two-dimensional framework through dimensionality reduction, making two-dimensional interpolation a representative paradigm. In this paper, a mathematical model is presented consideration of dimensionality reduction to derive the two-dimensional interpolation polynomial for the tabular function f(x, y). This model is further employed to analyze the interpolation error and determine the remainder term of the polynomial, which is then used to evaluate computational results and perform error estimation. Finally, an engineering example of two-dimensional interpolation is given. While the number of interpolation points is optimized, the proposed algorithm of two-dimensional interpolation yields accurate interpolation outcomes with reduced the complexity of computations. [ABSTRACT FROM AUTHOR]
Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Model of Lagrange Two-dimensional Interpolation Based on Dimensionality Reduction.
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  Data: <searchLink fieldCode="AR" term="%22Zhihua+Feng%22">Zhihua Feng</searchLink><relatesTo>1,2</relatesTo><i> fzh@djtu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Dayong+Zhou%22">Dayong Zhou</searchLink><relatesTo>3</relatesTo><i> zhoudy102@163.com</i>
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  Data: <searchLink fieldCode="JN" term="%22IAENG+International+Journal+of+Applied+Mathematics%22">IAENG International Journal of Applied Mathematics</searchLink>. Jul2025, Vol. 55 Issue 7, p2330-2335. 6p.
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  Data: <searchLink fieldCode="DE" term="%22Numerical+functions%22">Numerical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Two-dimensional+models%22">Two-dimensional models</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Data interpolation is a common challenge in both scientific research and engineering. Multidimensional interpolation, which encompasses one-dimensional interpolation as a subset, covers a broader range of problems. Notably, interpolation issues in dimensions higher than three can be reduced to a two-dimensional framework through dimensionality reduction, making two-dimensional interpolation a representative paradigm. In this paper, a mathematical model is presented consideration of dimensionality reduction to derive the two-dimensional interpolation polynomial for the tabular function f(x, y). This model is further employed to analyze the interpolation error and determine the remainder term of the polynomial, which is then used to evaluate computational results and perform error estimation. Finally, an engineering example of two-dimensional interpolation is given. While the number of interpolation points is optimized, the proposed algorithm of two-dimensional interpolation yields accurate interpolation outcomes with reduced the complexity of computations. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of IAENG International Journal of Applied Mathematics is the property of International Association of Engineers (IAENG) and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 6
        StartPage: 2330
    Subjects:
      – SubjectFull: Numerical functions
        Type: general
      – SubjectFull: Interpolation
        Type: general
      – SubjectFull: Mathematical models
        Type: general
      – SubjectFull: Two-dimensional models
        Type: general
      – SubjectFull: Polynomials
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      – TitleFull: Model of Lagrange Two-dimensional Interpolation Based on Dimensionality Reduction.
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              M: 07
              Text: Jul2025
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              Y: 2025
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