%% Example 1. Newton interpolating polynomial
clear all, clc ,close all, format compact, format
xnodes=[1:7]; ynodes=[2.3,3.4,5.1,6.3,7.5,8.2,7.4];
𝒇 𝒙𝟏, 𝒙𝟐 =
𝒇𝟐 − 𝒇𝟏
𝒙𝟐 − 𝒙𝟏
 …… …. ….
𝒇 𝒙𝟏, 𝒙𝟐, 𝒙𝟑 =
𝒇 𝒙𝟐, 𝒙𝟑 − 𝒇 𝒙𝟏, 𝒙𝟐
𝒙𝟑 − 𝒙𝟏
 …… …. ….
4
Newton interpolating polynomial
coef=ynodes; % determination of 𝒂𝟏, 𝒂𝟐, …
for k = 2:7
 coef(k:7) = (coef(k:7) - coef(k-1:6))./…
 (xnodes(k:7) - xnodes(1:8-k));
end
syms x
pol= coef(7); % coefficients of the polynomial
for k = 6:-1:1
 pol=pol*(x-xnodes(k))+coef(k);
end
𝒙𝒋 𝒇𝒋 𝒇 𝒙𝒋
, 𝒙𝒋+𝟏 𝒇 𝒙𝒋
, 𝒙𝒋+𝟏, 𝒙𝒋+𝟐 𝒇 𝒙𝒋
, 𝒙𝒋+𝟏, 𝒙𝒋+𝟐, 𝒙𝒋+𝟑
𝒙𝟏 𝒂𝟏 = 𝒇𝟏
𝒂𝟐 = 𝒇 𝒙𝟏, 𝒙𝟐
𝒙𝟐 𝒇𝟐 𝒂𝟑 = 𝒇 𝒙𝟏, 𝒙𝟐, 𝒙𝟑
𝒇 𝒙𝟐, 𝒙𝟑 𝒂𝟒 = 𝒇 𝒙𝟏, 𝒙𝟐, 𝒙𝟑, 𝒙𝟒
𝒙𝟑 𝒇𝟑 𝒇 𝒙𝟐, 𝒙𝟑, 𝒙𝟒
𝒇 𝒙𝟑, 𝒙𝟒
𝒙𝟒 𝒇𝟒
polyn=collect(pol)
coefpol=sym2poly(polyn) % coefficients of the polynomial (format double)