Interpolation Methos for Tensor Functions

Abstract

In this chapter polynomial interpolation is considered and extended to tensor-valued functions of one and two argument tensors. Let x_α(α = 1,2,...,n) be distinct points and y_α corresponding values. The polynomial of degree n-1

$$$$

(1)

is called “LAGRANGE interpolation formula”, where the polynomials

$$$$

(2)

are introduced. It is clear that L_α(x_β) is equal to one for α = β and equal to zero for α ≢ β. The remainder in (1) is given by

$$$$

(3)

where min (x, x₁,..., x_n) < ξ < max (x, x_l,..., x_n).