matlab 二分法程序

以下是一个简单的Matlab二分法程序的示例：

function [root, fx, ea, iter] = bisect(func, xl, xu, es, maxit)
% bisect: root location zeroes
% [root, fx, ea, iter] = bisect(func, xl, xu, es, maxit): uses bisection
% method to find the root of func
% input:
% func = name of function
% xl, xu = lower and upper guesses
% es = desired relative error (default = 0.0001%)
% maxit = maximum allowable iterations (default = 50)
% output:
% root = real root
% fx = function value at root
% ea = approximate relative error (%)
% iter = number of iterations

% check for proper sign change
test = func(xl) * func(xu);
if test > 0
    error('no sign change')
end

% set defaults
if nargin < 4 || isempty(es)
    es = 0.0001;
end
if nargin < 5 || isempty(maxit)
    maxit = 50;
end

% initialization
iter = 0;
xr = xl;
ea = 100;

% loop
while (1)
    xrold = xr;
    xr = (xl + xu) / 2;
    iter = iter + 1;
    if xr ~= 0
        ea = abs((xr - xrold) / xr) * 100;
    end
    test = func(xl) * func(xr);
    if test < 0
        xu = xr;
    elseif test > 0
        xl = xr;
    else
        ea = 0;
    end
    if ea <= es || iter >= maxit
        break
    end
end

% output
root = xr;
fx = func(xr);

end

这个程序使用了bisection方法来寻找函数的根。它需要输入函数名，下限和上限猜测值，所需的相对误差和最大迭代次数。输出是根，函数值，近似相对误差和迭代次数。