# 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:
');

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%Neville Method

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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.

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%Output%

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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.