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
时间: 2024-02-03 11:02:12 浏览: 27
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。
相关问题
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。
write a C program using full Muller-Brent algorithm to find the roots
Sure, I can help you with that. Here is an example C program that uses the full Muller-Brent algorithm to find the roots:
```
#include <stdio.h>
#include <math.h>
double f(double x) {
return x * sin(x) - 1;
}
double muller_brent(double a, double b, double c, double tol) {
double fa = f(a);
double fb = f(b);
double fc = f(c);
double d, e, q, r, p;
double denom, eps, tol1, xm;
int iter = 0;
do {
denom = (b - a) * (c - b) * (c - a);
eps = 1e-20;
tol1 = tol * fabs(b) + eps;
xm = 0.5 * (a + b);
if (fabs(fc) < fabs(fb)) {
a = b; b = c; c = a;
fa = fb; fb = fc; fc = fa;
}
q = (a - xm) * (fb - fc);
r = (b - xm) * (fa - fc);
p = (b - a) * (fa - fc);
d = 2.0 * p - sign(p) * (q - r);
e = sign(b - a) * sign(fa - fb) * fabs(q - r);
if (fabs(denom) > eps) {
d /= denom;
e /= denom;
} else {
d = e = 0;
}
if (fabs(e) < tol1 || iter > 100) {
b += sign(b - a) * tol1;
return b;
}
if (fabs(d) < tol1) {
xm = b + sign(b - a) * tol1;
} else if (d > 0) {
xm = b - e / (d + sqrt(d * d - 4.0 * p * e));
} else {
xm = b - 2.0 * p / (d - sqrt(d * d - 4.0 * p * e));
}
if (isnan(xm) || isinf(xm)) {
xm = (a + b) / 2;
}
double fxm = f(xm);
a = b;
b = xm;
fa = fb;
fb = fxm;
iter++;
} while (iter <= 100);
return NAN;
}
int main() {
double root = muller_brent(0, 2.0, 4.0, 1e-9);
printf("root = %f\n", root);
return 0;
}
```
This program defines a function `f(x)` that takes a single input variable `x` and returns the value of the function `x * sin(x) - 1`. It then uses the Muller-Brent algorithm to find a root of this function in the interval `[0, 2.0, 4.0]` with a tolerance of `1e-9`. The `sign` function used in the algorithm is defined as:
```
double sign(double x) {
return (x >= 0.0) ? 1.0 : -1.0;
}
```
相关推荐
![rar](https://img-home.csdnimg.cn/images/20210720083606.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)