牛顿法求解非线性方程组matlab源程序

牛顿法求解非线性方程组matlab源程序

Newton-Raphson 求解非线性方程组matlab源程序

matlab程序如下：

function hom

[P,iter,err]=newton('f','JF',[7.8e-001;4.9e-001; 3.7e-001],0.01,0.001,1000);

disp(P);

disp(iter);

disp(err);

function Y=f(x,y,z)

Y=[x^2+y^2+z^2-1;

2*x^2+y^2-4*z;

3*x^2-4*y+z^2];

function y=JF(x,y,z)

f1='x^2+y^2+z^2-1';

f2='2*x^2+y^2-4*z';

f3='3*x^2-4*y+z^2';

df1x=diff(sym(f1),'x');

df1y=diff(sym(f1),'y');

df1z=diff(sym(f1),'z');

df2x=diff(sym(f2),'x');

df2y=diff(sym(f2),'y');

df2z=diff(sym(f2),'z');

df3x=diff(sym(f3),'x');

df3y=diff(sym(f3),'y');

df3z=diff(sym(f3),'z');

j=[df1x,df1y,df1z;df2x,df2y,df2z;df3x,df3y,df3z];

y=(j);

function [P,iter,err]=newton(F,JF,P,tolp,tolfp,max)

%输入P为初始猜测值，输出P则为近似解

%JF为相应的Jacobian矩阵

%tolp为P的允许误差

%tolfp为f(P)的允许误差

%max：循环次数

Y=f(F,P(1),P(2),P(3));

for k=1:max

J=f(JF,P(1),P(2),P(3));

Q=P-inv(J)*Y;

Z=f(F,Q(1),Q(2),Q(3));

err=norm(Q-P);

P=Q;

Y=Z;

iter=k;

if (errbreak

end

end

function   homework4
[P,iter,err]=newton('f','JF',[7.8e-001;4.9e-001; 3.7e-001],0.01,0.001,1000);
disp(P);
disp(iter);
disp(err);
function Y=f(x,y,z)
Y=[x^2+y^2+z^2-1;
2*x^2+y^2-4*z;
3*x^2-4*y+z^2];
function y=JF(x,y,z)
f1='x^2+y^2+z^2-1';
f2='2*x^2+y^2-4*z';
f3='3*x^2-4*y+z^2';
df1x=diff(sym(f1),'x');
df1y=diff(sym(f1),'y');
df1z=diff(sym(f1),'z');
df2x=diff(sym(f2),'x');
df2y=diff(sym(f2),'y');
df2z=diff(sym(f2),'z');
df3x=diff(sym(f3),'x');
df3y=diff(sym(f3),'y');
df3z=diff(sym(f3),'z');
j=[df1x,df1y,df1z;df2x,df2y,df2z;df3x,df3y,df3z];
y=(j);
function [P,iter,err]=newton(F,JF,P,tolp,tolfp,max)
%输入P为初始猜测值，输出P则为近似解
%JF为相应的Jacobian矩阵
%tolp为P的允许误差
%tolfp为f(P)的允许误差
%max：循环次数
Y=f(F,P(1),P(2),P(3));
for k=1:max
J=f(JF,P(1),P(2),P(3));
Q=P-inv(J)*Y;
Z=f(F,Q(1),Q(2),Q(3));
err=norm(Q-P);
P=Q;
Y=Z;
iter=k;
if (errbreak
end
            

				

					
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