function Bisect2(a,b,nmax,emax)
% Cheney/Kincaid 5th Ed., Page 95.
% Bisection with a maximum number of iterations and
% a fixed value for epsilon.
% [Remember that "eps" is a reserved name in MATLAB!]
% I used:
% Bisect2(1.4,1.5,100,1e-20)
tic
% This function will approx sqrt(2).
% Inputs:  a < sqrt(2) < b.
% nmax = maximum number of iterations.
% emax = our max error
f = @(x) x^2 - 2;
% Initialize the end points.
fa = f(a);
fb = f(b);
if sign(fa)==sign(fb)
    fprintf('Function has same signs at a & b!\n');
    stop;
end
% Initialize error.
error = b - a;
% Print them out.
fprintf('  a  = %20.17f\n',a);
fprintf('  b  = %20.17f\n',b);
fprintf('f(a) = %20.17f\n',fa);
fprintf('f(b) = %20.17f\n',fb);
fprintf('Initial error = %20.17f\n',error);
% We will run nmax iterations (or fewer).
for i=0:nmax
    % Calculate the new error and new values for c & f(c).
    error = error/2.;
    c = a + error;
    fc = f(c);
    % If the abs. error is small enough, then we have converged.
    % Print out the results.
    if abs(error)<emax
        fprintf('Convergence achieved!\n');
        fprintf('Iteration #%5.0f\n',i);
        fprintf('   c  = %20.17f\n',c);
        fprintf(' f(c) = %20.17f\n',fc);
        fprintf('error = %24.17e\n',error);
        toc
        return;
    end
    % Adjust the end points according to the algorithm.
    % The logical operator "~=" is "not equal".
    if sign(fa)~=sign(fc)
        b = c;
        fb = fc;
    else
        a = c;
        fa = fc;
    end
end
% We've run out of iterations!
fprintf('Did not converge!\n');
fprintf('Iteration #%5.0f\n',nmax);
fprintf('   c  = %20.17f\n',c);
fprintf(' f(c) = %20.17f\n',fc);
fprintf('error = %24.17e\n',error);
toc