Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach

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...

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Vydáno v:Journal of applied mathematics Ročník 2022; s. 1 - 8
Hlavní autoři: Essanhaji, A., Errachid, M.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Hindawi 14.03.2022
John Wiley & Sons, Inc
Wiley
Témata:
Algorithms
Data points
Interpolation
Multivariate analysis
Polynomials
ISSN:1110-757X, 1687-0042
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1110-757X
1687-0042
DOI:10.1155/2022/8227086