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3. lagrange polynomial algorithm by neville interpolation at a vector of...

# Question: lagrange polynomial algorithm by neville interpolation at a vector of...

###### Question details

%Lagrange Polynomial Algorithm by
%Neville Interpolation at a vector of %points.
clc;
clear;
format long
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%Input
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n = input('Enter the number of points to interpolate at: ');
x = input('Enter the vector of points to interpolate at: ');

d = input('Enter the vector of function values of interpolation points: ');
t = input('Enter the value to approximate the function at: ');
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Neville Method
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q = zeros(n,n); %Initializes an n x n matrix
Q(:,1) = d'; %Enters the vector of

% function values as the first column of Q.

for i = 2:n
for j = 2:i
Q(i,j) =[(t - x(i - 1))*Q(i,j-1) - (t - x(i))*Q(i-1,j-1)]/(x(i) - x(i-1));
end
end
%Q(i,j) calculates the polynomial approximation for each matrix point.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Output%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Q%Displays the complete matrix Q.
P = input('Enter the point in the matrix to be outputed: ');
disp('The value of the polynomial is approximately: ')
disp(P) %Displays the function approximation for that Lagrange
%polynomial.   ###### Solution by an expert tutor 