Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach

A. Essanhaji and M. Errachid

Journal of Applied Mathematics, 2022, vol. 2022, issue 1

Abstract: The problems of polynomial interpolation with several variables present more difficulties than those of one‐dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well‐known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different generalizations and practical algorithms. The Newton basis format, with divided‐difference algorithm for coefficients, generalizes in a straightforward way when interpolating at nodes on a grid within certain schemes. In this work, we propose a random algorithm for computing several interpolating multivariate Lagrange polynomials, called RLMVPIA (Random Lagrange Multivariate Polynomial Interpolation Algorithm), for any finite interpolation set. We will use a Newton‐type polynomials basis, and we will introduce a new concept called (Z, z)‐partition. All the given algorithms are tested on examples. RLMVPIA is easy to implement and requires no storage.

Date: 2022
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https://doi.org/10.1155/2022/8227086

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2022:y:2022:i:1:n:8227086

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