Recursive polynomial interpolation algorithm (RPIA)

Abstract

Let x 0, x 1, ⋯ , x n be a set of n+1 distinct real numbers (i.e., x i ≠ x j for i ≠ j) and y 0, y 1, ⋯ , y n be given real numbers; we know that there exists a unique polynomial p n (x) of degree n such that p n (x i ) = y i for i = 0, 1, ⋯ , n; p n is the interpolation polynomial for the set {(x i , y i ), i = 0, 1, ⋯ , n}. The polynomial p n (x) can be computed by using the Lagrange method or the Newton method. This paper presents a new method for computing interpolation polynomials. We will reformulate the interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the recursive polynomial interpolation algorithm (RPIA). Some properties of this algorithm will be studied and some examples will also be given.