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

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Bibliographic Details
Title:	Model of Lagrange Two-dimensional Interpolation Based on Dimensionality Reduction.
Authors:	Zhihua Feng^1,2 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]
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Database:	Engineering Source

Description
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]
ISSN:	19929978