Newton Raphson Method

Jan 23, 2018 • Arne Vogel

The Newton-Raphson method (named after Isaac Newton 1669 and Joseph Raphson 1690) is a method for generating a numerical sulution for systems of equations.

Example for f(x) = -1/4x^4+5/2x^3-7x^2+8x-1, x0 = 2 and eps = 0.1 generated with MatLab:

Newton Raphson Method in MatLab

MatLab implementation for input:

function y = newton_raphson_method(f,x,x0,eps)
    fx = jacobian(f,x);
    v = num2cell(x0);
    b = f(v{:});

    while norm(b) > eps
        d = fx(v{:})\f(v{:});
        x0 = x0 - d;
        v = num2cell(x0);
        b = f(v{:});
    y = x0;

Note that the MatLab implementation doesn’t exit when the function has no root.

Download: newton_raphson_method.m

See newton_raphson_method_usage.m for how to use the implementation. You need the Symbolics library.