function Bisect1(a,b,nmax)
% Cheney/Kincaid 5th Ed., Page 94.
% Bisection with a maximum number of iterations.
% I used:
% Bisect1(1.4,1.5,100)
tic
% This function will approx sqrt(2).
% Inputs:  a < sqrt(2) < b.
% nmax = maximum number of iterations.
%
% This is called a function "handle".
% This defines f(x).
f = @(x) x^2 - 2;
% Initialize the end points.
u = f(a);
v = f(b);
% Cheney says to print them out.
fprintf(' a = %20.17f\n',a);
fprintf(' b = %20.17f\n',b);
fprintf(' u = %20.17f\n',u);
fprintf(' v = %20.17f\n',v);
if (u*v)>=0
    fprintf(' Poor choice of [a,b]:  u*v is >=0.\n');
end
% We will run nmax iterations (or fewer).
for i=0:nmax
    % Calculate the midpoint of the current interval.
    % Calculate f at that point.
    c = (a + b)/2.;
    w = f(c);
    % If (w*u) is machine zero, then stop!
    if (w*u)==0.
        fprintf(' Iteration #%5.0f\n',i);
        fprintf(' Midpoint = %20.17f\n',c);
        fprintf(' f(c) = %20.17f\n',w);
        return;
    else
        if (w*u) < 0.
            % If w*u is neg. then redefine the right end
            % of the interval.
            b = c;
            v = w;
        else
            % w*u must be pos.; so redefine the left end
            % of the interval.
            a = c;
            u = w;
        end 
    end
end
% Print the final value of c & f(c).
fprintf(' Iteration #%5.0f\n',nmax);
fprintf(' Midpoint = %20.17f\n',c);
fprintf(' f(c) = %20.17f\n',w);
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