Obtaining Exact Interpolation Multivariate Polynomial by Approximation

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.