In the mathematical field of numerical analysis, a Newton polynomial, named after its inventor Isaac Newton, is an interpolation polynomial for a given set of data points. The Newton polynomial is sometimes named Newton's divided differences interpolation polynomial because the coefficients of the polynomial are calculated use Newton's divided differences method.

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```
%Newton's method is one of the fastest algorithms to converge on a root.
%It does not require you to provide any endpoints, but it does require for
%you to provide the derivative of the function. It is faster than the secant
%method, but is also not guaranteed to converge.
%INPUTS:
%function handle f
%function handle df for the derivative of f
%initial x-value
%maximum tolerated error
%OUTPUTS:
%An approximated value for the root of f.
%Written by MatteoRaso
function y = newton(f, df, x, error)
while abs(f(x)) > error
x = x - f(x) / df(x);
disp(f(x))
endwhile
A = ["The root is approximately located at ", num2str(x)];
disp(A)
y = x;
endfunction
```