给出matlab的二分法求根的代码

以下是一个简单的 Matlab 代码示例，使用二分法求解函数 $f(x)$ 的根：

function [root, fx, ea, iter] = bisection(f, xl, xu, es, maxit)
% Bisection method for root finding
% Input:
%   - f: the function handle to the function to be solved
%   - xl, xu: the lower and upper bounds of the interval containing the root
%   - es: the desired relative error (default: 0.0001%)
%   - maxit: the maximum number of iterations (default: 50)
% Output:
%   - root: the estimated root of f(x)
%   - fx: the function value at the root
%   - ea: the approximate relative error (%)
%   - iter: the number of iterations performed

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

% check if the root is bracketed
if f(xl) * f(xu) > 0
    error('The root is not bracketed!');
end

% initialize variables
iter = 0;
xr = xl;
ea = 100;

% main loop
while ea > es && iter < maxit
    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

% output results
root = xr;
fx = f(xr);

end

使用示例：

% define the function to be solved
f = @(x) x^2 - 2;

% call the bisection function
[root, fx, ea, iter] = bisection(f, 0, 2, 0.0001, 50);

% display results
fprintf('Root: %f\n', root);
fprintf('Function value: %f\n', fx);
fprintf('Approximate relative error: %f%%\n', ea);
fprintf('Number of iterations: %d\n', iter);

其中，`f` 是要求解根的函数句柄，`xl` 和 `xu` 是根所在的区间的下限和上限，`es` 是期望的相对误差，`maxit` 是最大迭代次数。函数返回根 `root`、函数值 `fx`、近似相对误差 `ea` 和迭代次数 `iter`。