Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach

A. Essanhaji, M. Errachid and Saeid Abbasbandy

Journal of Applied Mathematics, 2022, vol. 2022, 1-8

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:8227086

DOI: 10.1155/2022/8227086

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