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function [root, fx, ea, iter] = falsePosition(func, xl, xu, es, maxit, varargin)
%falsePosition finds the root of a function using false position method
% Syntax:
% [root, fx, ea, iter] = falsePosition(func, xl, xu, es, maxit, varargin)
%
% Input:
% func = function being evaluated
% xl = lower guess
% xu = upper guess
% es = desired relative error (default 0.0001%)
% maxit = maximum number of iterations (default 200)
% varargin, ...= any additional parameters used by the function
% Output:
% root = estimated root location
% fx = function evaluated at root location
% ea = approximated relative error (%)
% iter = number of iterations performed
if nargin < 3, error('Too few arguments: at least 3 needed'), end
if nargin < 4 | isempty(es), es = 0.0001; end
if nargin < 5 | isempty(maxit), maxit = 200; end
iter = 0;
ea = 100;
xr = xl;
while(1)
xrold = xr;
iter = iter + 1;
xr = (xl * func(xu) - xu * func(xl))/(func(xu)-func(xl));
if xr~= 0
ea = abs((xr-xrold)/xr)*100;
end
if func(xl)*func(xr)<0
xu = xr;
else
xl = xr;
end
if iter == maxit | ea <= es, break, end
end
root = xr;
fx = func(xr,varargin{:});
ea = ea;
iter = iter;
end
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