interpolée un polynome avec la méthode de newton in matlab

To interpolate a polynomial using the Newton method in Matlab, you can use the polyfit function.

Let's say we have a set of data points (x,y) that we want to interpolate using a polynomial of degree n. The steps to perform Newton interpolation in Matlab are:

1. Define the data points (x,y) as vectors:

main.m
x = [x1, x2, ..., xn];
y = [y1, y2, ..., yn];
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2. Use the polyfit function with the argument n to obtain the coefficients that define the polynomial of degree n that best fits the data points:

main.m
coefficients = polyfit(x, y, n);
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3. Evaluate the polynomial at any point x using the coefficients obtained in step 2:

main.m
y_interp = polyval(coefficients, x_interp);
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Where x_interp is the point where we want to interpolate the polynomial, and y_interp is the interpolated value.

Here's an example of how to perform Newton interpolation in Matlab:

main.m
% Define the data points
x = [1, 2, 3, 4, 5];
y = [2, 4, 1, 6, 3];

% Define the degree of the polynomial to fit
n = 4;

% Use the polyfit function to obtain the coefficients of the polynomial
coefficients = polyfit(x, y, n);

% Evaluate the polynomial at a point x_interp
x_interp = 2.5;
y_interp = polyval(coefficients, x_interp);

% Plot the original data and the interpolated point
plot(x, y, 'o', x_interp, y_interp, 'x')
legend('Data points', 'Interpolated point')
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This will plot the original data points and the interpolated point at x=2.5 using a polynomial of degree 4.