基于符号数值计算的代数曲线区间插值

Algebraic curve interpolation is described by specifying the location of N points in the plane and constructing an algebraic curve of function f that passes 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, we also present 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, including an example to recover Kepler’s third law of planet motion by analyzing the orbital data of 38 planets, asteroids, and dwarfs.