求非线性方程组matlab算法
时间: 2023-12-06 08:37:13 浏览: 37
以下是几种求解非线性方程组的Matlab算法:
1. 对称秩1算法
```matlab
function [x, k] = mulRank1(f, x0, eps)
% f为非线性方程组,x0为初始点,eps为精度
% x为方程组的一个根,k为迭代次数
n = length(x0);
B = eye(n);
x = x0;
k = 0;
while norm(f(x)) > eps
p = -B * f(x);
alpha = 1;
while norm(f(x + alpha * p)) >= norm(f(x))
alpha = alpha / 2;
end
s = alpha * p;
y = f(x + s) - f(x);
B = B + (y - B * s) * s' * B / (s' * B * s);
x = x + s;
k = k + 1;
end
end
```
2. D-F-P算法
```matlab
function [x, k] = mulDFP(f, x0, eps)
% f为非线性方程组,x0为初始点,eps为精度
% x为方程组的一个根,k为迭代次数
n = length(x0);
B = eye(n);
x = x0;
k = 0;
while norm(f(x)) > eps
p = -B * f(x);
alpha = 1;
while norm(f(x + alpha * p)) >= norm(f(x))
alpha = alpha / 2;
end
s = alpha * p;
y = f(x + s) - f(x);
B = B + (y * y') / (y' * s) - (B * s * s' * B) / (s' * B * s);
x = x + s;
k = k + 1;
end
end
```
3. B-F-S算法
```matlab
function [x, k] = mulBFS(f, x0, eps)
% f为非线性方程组,x0为初始点,eps为精度
% x为方程组的一个根,k为迭代次数
n = length(x0);
B = eye(n);
x = x0;
k = 0;
while norm(f(x)) > eps
p = -B \ f(x);
alpha = 1;
while norm(f(x + alpha * p)) >= norm(f(x))
alpha = alpha / 2;
end
s = alpha * p;
y = f(x + s) - f(x);
B = B + ((y - B * s) * (y - B * s)') / ((y - B * s)' * s);
x = x + s;
k = k + 1;
end
end
```
4. 数值延拓法
```matlab
function [x, k] = mulNumYT(f, x0, eps)
% f为非线性方程组,x0为初始点,eps为精度
% x为方程组的一个根,k为迭代次数
n = length(x0);
x = x0;
k = 0;
while norm(f(x)) > eps
J = jacobianest(f, x);
s = -J \ f(x);
x = x + s;
k = k + 1;
end
end
```
5. 参数微分法
```matlab
function [x, k] = DiffParam1(f, x0, eps)
% f为非线性方程组,x0为初始点,eps为精度
% x为方程组的一个根,k为迭代次数
n = length(x0);
x = x0;
k = 0;
while norm(f(x)) > eps
J = zeros(n);
for i = 1:n
h = 1e-6;
x1 = x;
x1(i) = x1(i) + h;
J(:, i) = (f(x1) - f(x)) / h;
end
s = -J \ f(x);
x = x + s;
k = k + 1;
end
end
```