New algorithm for computing the Hermite interpolation polynomial

作者：Messaoudi A^*; Sadaka R; Sadok H

来源：Numerical Algorithms, 2018, 77(4): 1069-1092.

DOI：10.1007/s11075-017-0353-6

• Polynomial interpolation
• Hermite interpolation polynomials
• Schur complement
• Matrix Sylvester identity
• Recursive polynomial interpolation algorithm
• Matrix recursive interpolation algorithm

Let x (0), x (1),ai , x (n) , be a set of n + 1 distinct real numbers (i.e., x (i) not equal x (j) , for i not equal j) and y (i, k) , for i = 0,1,ai , n, and k = 0 ,1 ,ai , n (i) , with n (i) ae 1, be given of real numbers, we know that there exists a unique polynomial p (N - 1)(x) of degree N - 1 where , such that , for i = 0,1,ai , n and k = 0,1,ai , n (i) . P (N-1)(x) is the Hermite interpolation polynomial for the set {(x (i) , y (i, k) ), i = 0,1,ai , n, k = 0,1,ai , n (i) }. The polynomial p (N-1)(x) can be computed by using the Lagrange polynomials. This paper presents a new method for computing Hermite interpolation polynomials, for a particular case n (i) = 1. We will reformulate the Hermite interpolation polynomial problem and give a new algorithm for giving the solution of this problem, the Matrix Recursive Polynomial Interpolation Algorithm (MRPIA). Some properties of this algorithm will be studied and some examples will also be given.

• 出版日期2018-4