unction [R] = Muller(f, ~,x0, x1, x2, iter, tol) %MULLER Solving a nonlinear equation with one variable. % Using interpolation with three points to approximate the root. % INPUTS: % x0, x1, x2: initial values (x2 is the best, x0 is the worst) % iter: number of iteration % tol: error tolerance for reltive error % f: left-hand side of the nonlinear equation % OUTPUTS: % x2: the approximate root k = 0; R = {1, 1}; while k<iter && abs((x2-x1)/x1)>tol omega = (f(x2)-f(x1))/(x2-x1); d = f(x0)/((x0-x1)*(x0-x2))+f(x1)/((x1-x0)*(x1-x2))+f(x2)/((x2-x1)*(x2-x0)); omega = omega+d*(x2-x1); x0 = x1; x1 = x2; x2 = x2-2*f(x2)/(omega+sign(omega)*sqrt(omega^2-4*f(x2)*d)); k = k+1; R{1, k} = x2; end R = cell2mat(R); end

这是一个求解非线性方程的 Muller 方法的 MATLAB 函数，它使用三个初始点进行插值来逼近根。

输入参数包括：

- f: 代表非线性方程左侧的函数句柄
- x0, x1, x2: 三个初始点
- iter: 迭代次数
- tol: 相对误差容忍度

输出参数为：

- R: 迭代过程中的所有近似根，以向量形式返回

函数的具体实现过程如下：

1. 初始化迭代参数和近似根：

k = 0;
R = {1, 1};

2. 在迭代次数和相对误差容忍度内进行循环，更新近似根：

while k<iter && abs((x2-x1)/x1)>tol
    omega = (f(x2)-f(x1))/(x2-x1);
    d = f(x0)/((x0-x1)*(x0-x2))+f(x1)/((x1-x0)*(x1-x2))+f(x2)/((x2-x1)*(x2-x0));
    omega = omega+d*(x2-x1);
    x0 = x1;
    x1 = x2;
    x2 = x2-2*f(x2)/(omega+sign(omega)*sqrt(omega^2-4*f(x2)*d));
    k = k+1;
    R{1, k} = x2;
end

3. 将近似根转换为向量并返回：

R = cell2mat(R);

希望这能帮助您理解该函数的实现过程。