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734089118

新虫 (初入文坛)

[求助] 牛顿法求解非线性方程组无法得出结果,求助~~ 已有1人参与

%Newton法解非性
clear
clear all
clc
N=3;
x0=[0.3,0.7,1.4]';
x=x0;
F=zeros(N,1);
tic
for s=1:1:100

F(1)=cos(x(1))+cos(x(2))+cos(x(3))-pi*3*0.8/4;
F(2)=cos(5*x(1))+cos(5*x(2))+cos(5*x(3));
F(3)=cos(7*x(1))+cos(7*x(2))+cos(7*x(3));
jacobi=[-sin(x(1)),-sin(x(2)),-sin(x(3));-5*sin(x(1)),-5*sin(x(2)),-5*sin(x(3));-7*sin(x(1)),-7*sin(x(2)),-7*sin(x(3))];

x_n=x-jacobi^(-1)*F;
if sum(abs(x_n-x))<0.000001
    break
end
x=x_n;
end
s
x
F
a=toc
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wurongjun

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【答案】应助回帖

感谢参与,应助指数 +1
首先,牛顿迭代法是初值敏感的!初值要靠近解才可能收敛!
另外,要保证雅可比矩阵非奇异才行!
善恶到头终有报,人间正道是沧桑.
2楼2015-05-30 00:46:34
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feixiaolin

荣誉版主 (文坛精英)

优秀版主

有多组解,如:
目标函数值: 2.83034706782814E-12
x1: 0.510255698326351
x2: 0.950128345330017
x3: 1.12546462681943

目标函数值: 8.88147888566948E-12
x1: 1.12546462681966
x2: 5.77292960885286
x3: 7.23331365250866

目标函数值: 9.18409792660668E-12
x1: 1.12546462681809
x2: -0.950128345327862
x3: 0.510255698320529
3楼2015-05-31 14:59:39
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