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

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

Answer 1

[Nithin]

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)]);

I hope this answer helps you.

Regards,

Nithin Kumar.

[Torsten]

You should explain what "divdiff" is. It's not part of the MATLAB software.