write a C program using full Muller-Brent algorithm to find the roots
时间: 2023-05-22 12:03:02 浏览: 76
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相关问题
c语言如何通过Box-Muller方法生成正态分布数组
Box-Muller方法是一种用来生成正态分布随机数的方法,它可以通过将两个均匀分布的随机数转换为一组服从正态分布的随机数来实现。在C语言中,可以使用类似于以下的代码来实现Box-Muller方法:double u1, u2, w;
do {
u1 = 2 * (rand() / (double)RAND_MAX) - 1;
u2 = 2 * (rand() / (double)RAND_MAX) - 1;
w = u1 * u1 + u2 * u2;
} while (w >= 1);double z1 = sqrt(-2 * log(w) / w) * u1;
double z2 = sqrt(-2 * log(w) / w) * u2;
function [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
这是一段求解非线性方程的 Muller 方法的 MATLAB 函数。您之前的代码可能是因为没有给函数命名而导致出现未定义变量的错误。
该函数的输入参数包括:
- 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);
```
希望这能够帮助您理解该函数的实现过程。
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