Curve fitting using Newton divide-difference interpolation method on matlab

 Newton divided difference interpolation method

Newton's divided difference interpolation method is a numerical technique for finding a polynomial function that passes through a given set of data points. The polynomial function can be used to approximate the behavior of a given function or to interpolate data values between the given points.

The method involves constructing a set of divided differences based on the given data points. Divided differences are defined recursively in terms of lower-order differences until a table of all divided differences is generated. The coefficients of the polynomial function are then determined from the first row of the table.

% Curve fitting using the Newton-Divide difference method

% Input data points

x = [1 2 4 7];

y = [0 4 2 3];

% Number of data points

n = length(x);

% Initialize divided difference table

f = zeros(n);

% Assign y values to the first column of the divided difference table

f(:,1) = y';

% Calculate divided differences

for j = 2:n

for i = j:n

f(i,j) = (f(i,j-1) - f(i-1,j-1))/(x(i)-x(i-j+1));

end

end

% Polynomial coefficients are the diagonal elements of the divided difference table

coeffs = diag(f);

% Calculate polynomial function

syms t;

polynomial = coeffs(1);

for i = 2:n

term = 1;

for j = 1:i-1

term = term*(t-x(j));

end

polynomial = polynomial + coeffs(i)*term;

end

% Display polynomial function and polynomial coefficients

disp("Polynomial function:");

disp(polynomial);

disp("Polynomial coefficients:");

disp(coeffs);

=========================================================================

>>newton_divided_difference

Polynomial function:
4*t - (5*(t - 1)*(t - 2))/3 + (29*(t - 1)*(t - 2)*(t - 4))/90 - 4

Polynomial coefficients:
0
4.0000
-1.6667
0.3222