MATLAB Implementation of Newton Interpolation Method with Code Explanation

This MATLAB program implements Newton's interpolation method, which constructs a polynomial that exactly fits given data points. Newton interpolation is a numerical analysis technique for estimating unknown data values based on known discrete points.

The program executes through three main computational phases:

1. Data Point Input: Defines the known coordinate pairs

2. Divided Difference Table Calculation: Builds the foundation for polynomial coefficients using recursive difference formulas

3. Interpolation Computation: Evaluates the Newton polynomial at new x-coordinates

The complete implementation code is provided below. Execute this script in MATLAB environment.

```MATLAB

% Define input data points (x,y coordinates)

X = [1 2 4 7 8];

Y = [3 5 12 13 14];

% Compute divided difference table

n = length(X);

F = zeros(n,n);

F(:,1) = Y';

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

% Perform interpolation at new point

new_x = 5;

result = 0;

for i=1:n

temp = F(i,i);

for j=1:i-1

temp = temp*(new_x-X(j));

end

result = result+temp;

end

% Display interpolation result

disp(result);

```

Key algorithmic notes: The code constructs Newton's polynomial using divided differences (stored in matrix F), where diagonal elements F(i,i) represent polynomial coefficients. The nested loops implement the recursive difference calculation characteristic of Newton's method.

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