Multidimensional algebraic interpolations
Matvey Durakov, Evgeniy Leinartas, August Tsikh
TL;DR
This paper develops a multidimensional Hermite interpolation framework using algebraic systems and residues, providing explicit formulas for interpolation polynomials in higher dimensions.
Contribution
It introduces a novel class of algebraic systems enabling explicit formulas for multidimensional Hermite interpolation polynomials.
Findings
Explicit formulas for multidimensional Hermite interpolation polynomials
Use of multidimensional residues as a key theoretical tool
Extension of algebraic interpolation methods to higher dimensions
Abstract
The Hermite interpolation formulas are based on the interpretation of interpolation nodes as roots of suitable polynomials. Therefore, such formulas belong to the class of algebraic interpolations. The article considers a multidimensional variant of Hermite interpolation, presents a class of algebraic systems of equations for which the Hermite interpolation polynomial is represented by an explicit formula. The theory of multidimensional residues is used as the main tool.
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Taxonomy
TopicsAdvanced Theoretical and Applied Studies in Material Sciences and Geometry · Mechanical Systems and Engineering · Advanced Numerical Analysis Techniques