Question

Inverse Interpolation and Neville’s algorithm. (P. 142–144 of the 6th edition or P. 170–172 of the 7th edition of the textbook）

use Matlab

Answer 1

Inverse Interpolation: When n points were given as (f(xi ), xi ) we tried to determine the value of the function f(xk) for an intermediate value of the independent variable, xk • The inverse problem of this is to determine the value of the independent variable x for given value of f(x). • Such a process is known as inverse interpolation. Thus inverse interpolation is the process of finding the value of the argument corresponding to a given value of the function lying between two tabulated functional values.

Neville's algorithm: Neville's algorithm was derived by the mathematician Eric Harold Neville. Neville's algorithm is an interpolation algorithm that proceeds by first fitting a polynomial of degree 0. The main idea of Neville's algorithm is to approximate the value of a polynomial at a particular point without having to first find all of the coefficients of the polynomial.