I've recently wrote this Function M-file to find the root of any function using the secant method. I have a problem though, in that whenever i use the file on a function, i get the error
???Error using ==> secant at 34
convergence not achieved
Can anyone see why my file is doing this?
Here is the script:
function [x, iter] = secant( f, x0, x1, nmax, tol )
%SECANT Secant method for root finding.
% [X, ITER] = SECANT( F, X0, X1, NMAX, TOL ) finds a zero, X,
% of the function F(X) using the secant method. X0 and X1 are the
% initial values required for the secant method, NMAX is the
% maximum number of iterations allowed, and TOL is the convergence
% criterion. ITER is the number of iterations required.
% Test to make sure nmax and tol are valid.
if nmax < 1
error('nmax must be greater than 0')
if tol < eps
error('tol must be greater than or equal to eps')
% nmax >=1 and tol >= eps at this point.
%Set initial valies for x, iter and err.
x = x1;
iter = 0;
err = abs(x1-x0);
% The invariant for this loop is "iter is the number of iterations
% completed at the start of the loop".
% At the start of the loop, x0 and x1 are the first two points which will be
% used to extrapolate a secant line to the next value of x. The current
% approximation to the solution (after 0 iterations) is x = x1 and err is an
% upper bound for the error in x.
while err > tol
% Test for maximum number of iterations.
if iter == nmax;
error('convergence not achieved')
% Carry out one secant step.
fx1 = f(x1);
fx0 = f(x0);
x = x1 - (fx1*((x1 - x0)/(fx1 - fx0))); % Secant forumula
x1 = x0; % x1 is new value for x0
x = x1; % x is new value for x1
% Increment iter so that the invariant is preserved.
iter = iter + 1;
% Here, the while condition is false so err <= tol.
% From the loop invariant, iter is the number of iterations taken.