有限域上插值多项式的两种构造方法

在实数域上构造插值多项式,由于计算机精度的限制和存在舍入误差与截断误差,会使构造的插值多项式产生很大的误差。因此文章将问题限制在有限域上,给出了有限域上存在唯一的插值多项式的定理,且对定理进行了严格的证明。同时将Lagrange插值法与Newton插值法推广到有限域上,形成有限域上构造插值多项式的两种方法,最后通过算例验证了此方法的正确性。

Tow Construction Methods of Interpolation Polynomial in Finite Field

Interpolation polynomials established in real number field may bring large error because of the accuracy limitations,rounding error and truncation error of computers.Problems of interpolation polynomials is considered in finite field in this paper,a theorem about the existence and uniqueness of interpolation polynomial in finite field is proposed,and then the theorem is proved strictly.Then tow construction methods to gain the interpolation polynomials in finite field is also proposed by extending Lagrange interpolation and Newton interpolation to the finite field.At last,some examples are given to verify the correctness of the tow methods.