Obtaining Exact Interpolation Multivariate Polynomial by Approximation
Yong Feng, Jingzhong Zhang, Xiaolin Qin, Xun Yuan

TL;DR
This paper explores how to derive exact multivariate interpolation polynomials with rational coefficients using approximate interpolation methods, aiming to improve computational efficiency in symbolic mathematics and related fields.
Contribution
It introduces a novel approach to obtain exact interpolation polynomials via approximation techniques, reducing symbolic computation complexity.
Findings
Successfully derived exact polynomials from approximate methods
Reduced symbolic computation complexity
Applicable to multivariate polynomial interpolation
Abstract
In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exactly interpolating methods are often proposed for the exact results and approximate interpolating methods for the approximate ones. In this paper, we study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.
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Taxonomy
TopicsNumerical Methods and Algorithms · Polynomial and algebraic computation · Advanced Numerical Analysis Techniques
