Algebraic Curve Interpolation for Intervals via Symbolic-Numeric Computation

Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the algebraic curve that interpolates a set of data (points or nei...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Dehbi, Lydia, Yang, Zhengfeng, Chao, Peng, Xu, Yaochen, Zeng, Zhenbing
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 20.05.2024
Subjects:	Computation Interpolation Lagrange multiplier Mathematical analysis Polynomials
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of a function f that should pass through them. In this paper, we propose a novel approach to construct the algebraic curve that interpolates a set of data (points or neighborhoods). This approach aims to search the polynomial with the smallest degree interpolating the given data. Moreover, the paper also presents an efficient method to reconstruct the algebraic curve of integer coefficients with the smallest degree and the least monomials that interpolates the provided data. The problems are converted into optimization problems and are solved via Lagrange multipliers methods and symbolic computation. Various examples are presented to illustrate the proposed approaches.
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.2407.07095