function Secant1(a,b,nmax,ep)
% Cheney/Kincaid 5th Ed., Page 127.
% Secant Method with a maximum number of iterations and
% a fixed value for epsilon.
% You must provide a starting interval [a,b] = [x_0,x_1].
% nmax = max iterations
% ep = max error for convergence of d
tic
% We will use the example on p. 128.
% f(x) = x^5 + x^3 + 3  in [-1,1].
% I used:
% Secant1(-1,1,100,1e-10)
f = @(x) x^5 + x^3 + 3;
% Initialize f(a) & f(b).
fa = f(a);
fb = f(b);
% We must ensure that abs(fa)<=abs(fb).
% If necessary, swap a & b, using c & fc as temp storage.
if abs(fa) > abs(fb)
    c = a;
    a = b;
    b = c;
    fc = fa;
    fa = fb;
    fb = fc;
end
% I guess we can start a table.
fprintf('  n   x_n                   f(x_n)\n');
fprintf('  0  %20.17f  %20.17f\n',a,fa);
fprintf('  1  %20.17f  %20.17f\n',b,fb);
% We will run nmax iterations (or fewer).
for i=2:nmax
    % We must ensure that abs(fa)<=abs(fb).  [See above!]
    if abs(fa) > abs(fb)
        c = a;
        a = b;
        b = c;
        fc = fa;
        fa = fb;
        fb = fc;
    end
    % Calculate the new value of x for this iteration.
    d = (b - a)/(fb - fa);
    b = a;
    fb = fa;
    d = d*fa;
    % If abs(d) < epsilon, then we have convergence.
    if abs(d) < ep
        fprintf('Convergence; abs(d) < epsilon\n');
        toc
        return;
    end
    % Output the new value of x, which is now "a".
    a = a - d;
    fa = f(a);
    fprintf('%3d  %20.17f  %20.17f\n',i,a,fa);
end
% We've run out of iterations!
fprintf('Did not converge!\n');
toc