How to write a code which find the value of the Newton interpolation polynomial at a given point X0?

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Mehmet Talha Özvarinli 2021-12-8

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编辑： Torsten 2023-10-13

Hi, I wanna learn how can I implement this equation with matlab. Thanks to all.

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Answer 1

Nithin 2023-10-13

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Hi Mehmet,

I understand that you want to know the process of finding the value of Newton Interpolation polynomial at a point 'X0'.

To implement this, kindly refer to the following code snippet-

% Define your data points as vectors of X and Y values
X = [x1, x2, x3, ...];  % Input values
Y = [y1, y2, y3, ...]; 
% The point at which you want to evaluate the polynomial
X0 = your_desired_X0;
 
% Calculate the coefficients of the Newton polynomial
coeff = divdiff(X, Y); % Calculate the dividend differences
% Initialize the result
result = coeff(1);  % The first coefficient is f(x0)
% Evaluate the polynomial at X0 using nested multiplication
n = length(X) - 1;
for i = 1:n
    term = coeff(i + 1);
    for j = 1:i
        term = term * (X0 - X(j));
    end
    result = result + term;
end
disp(['The value of the Newton interpolation polynomial at X0 is: ' num2str(result)]);