bisection in matlab

main.m
function [root, fx, ea, iter] = bisection(f, xl, xu, es, maxiter)
% bisection: root finding via the bisection method
%   [root, fx, ea, iter] = bisection(f, xl, xu, es, maxiter):
%       uses the bisection method to find the root of function f
%       within the bracket [xl, xu]
% input:
%   f = the function to be evaluated
%   xl, xu = the lower and upper bounds of the bracket
%   es = the desired relative error (default: 0.0001%)
%   maxiter = the maximum number of iterations (default: 50)
% output:
%   root = the estimated root
%   fx = the function evaluated at the estimated root
%   ea = the approximate relative error (%)
%   iter = the number of iterations performed

% check number of inputs
if nargin < 3
    error('at least 3 input arguments required')
end
% set defaults
if nargin < 4 || isempty(es)
    es = 0.0001;
end
if nargin < 5 || isempty(maxiter)
    maxiter = 50;
end
% check bracket
test = f(xl) * f(xu);
if test > 0
    error('no sign change in bracket')
end
% initialize variables
iter = 0;
xr = xl;
ea = 100;
% loop until relative error is smaller than desired error or maxiter is reached
while ea > es && iter < maxiter
    xrold = xr;
    xr = (xl + xu) / 2;
    iter = iter + 1;
    if xr ~= 0
        ea = abs((xr - xrold) / xr) * 100;
    end
    test = f(xl) * f(xr);
    if test < 0
        xu = xr;
    elseif test > 0
        xl = xr;
    else
        ea = 0;
    end
end
% calculate function value at root
fx = f(xr);
% output results
root = xr;
end
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main.m
f = @(x) x^2 - 2;
xl = 1;
xu = 2;
es = 0.001;
maxiter = 100;
[root, fx, ea, iter] = bisection(f, xl, xu, es, maxiter);
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