% test_newton.m

% Example 1:	usual case, quadratic convergence
f = @(x) x^2 -2;
fp = @(x) 2*x;

% Example 2		root of multiplicity > 1, linear convergence
f = @(x) (x-5)^4;
fp = @(x) 4*(x-5)^3;

% Example 3		possibility of non-convergence
f = @(x) tanh(x);
fp = @(x) 1 - tanh(x)^2;

abstol = 1.0e-14
maxits = 20
x0 = 1.0
x0 = 1.09
r = newton(f,fp,x0,abstol,maxits)