solving non linear equations
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clc
clear all
syms x y z xn xnp
double err
int16 n;
err=10^-4
n=2;
f1= [ x^2+x-y^2+x*y+z^2-3
5*(y^2)+y+y*z-x^2+z-7
x+y+z+y*z-z^3-3]
g=jacobian([f1],[x,y,z])
t=inv(g)
xn=sym([0.5;0.5;0.5])
xnp=-xn
i=0
while max(abs(xnp-xn))> err
xn=xnp
fc=f1
jc=t
fc(xn)=subs(fc,[x;y;z],xn)
jc(xn)=subs(jc,[x;y;z],xn)
xnp=xn-(fc*jc)
fc=[]
jc=[]
fprintf('Iteration %d: x=%.18f',i, xnp);
i=i+1
end
i am tryin here to write my own code to solve non linear system based on Newton method am pretty sure about the algorithm and how to use the mehtod in solving non linear system however am not sure about the syntax of matlab coding . can anyone please help with an explanation of these errors and how to avoid them. thanks in advance .
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Respuestas (2)
VBBV
el 18 de Nov. de 2022
Editada: VBBV
el 18 de Nov. de 2022
fc(:,i+1)=subs(fc,[x;y;z],xn)
jc(:,i+1)=subs(jc,[x;y;z],xn)
3 comentarios
VBBV
el 18 de Nov. de 2022
clc
clear all
syms x y z xn xnp
double err;
int16 n;
err=10;
n=2;
f1= [ x^2+x-y^2+x*y+z^2-3
5*(y^2)+y+y*z-x^2+z-7
x+y+z+y*z-z^3-3];
g=jacobian([f1],[x,y,z]);
t=inv(g);
xn=sym([0.5;0.5;0.5]) ;
xnp=-xn;
i=0;
while max(abs(xnp-xn)) < err % check the condition
xn=xnp;
fc=f1;
jc=t;
fc(:,i+1)=subs(fc,[x;y;z],xn);
jc(:,:,i+1)=subs(jc,[x;y;z],xn); % use the iteration index i
xnp=xn-(fc(:,i+1)'*jc(:,:,i+1)).';
fprintf('Iteration %d:\n',i+1);
fprintf(' x=%.18f\n',xnp)
i=i+1;
end
Torsten
el 18 de Nov. de 2022
Editada: Torsten
el 18 de Nov. de 2022
syms x y z
errX = 10;
errF = 10;
imax = 25;
TolX = 1e-8;
TolF = 1e-8;
f = [ x^2+x-y^2+x*y+z^2-3
5*(y^2)+y+y*z-x^2+z-7
x+y+z+y*z-z^3-3];
J = jacobian(f,[x,y,z]);
Jinv = inv(J);
xi = [0.5;0.5;0.5] ;
i = 0;
while (errX > TolX || errF > TolF) && i < imax % check the condition
fi = double(subs(f,[x y z],[xi(1) xi(2) xi(3)]));
Ji = double(subs(Jinv,[x y z],[xi(1) xi(2) xi(3)]));
xip1 = xi - Ji*fi;
i = i + 1;
errX = max(abs(xip1-xi))
errF = norm(fi)
fprintf('Iteration %d:\n',i);
fprintf(' x=%.18f\n',xi)
fprintf(' f=%.18f\n',fi)
xi = xip1;
end
4 comentarios
Torsten
el 26 de Nov. de 2022
Editada: Torsten
el 26 de Nov. de 2022
I set xi to the gams solution and your code confirmed it.
Now you can try to set the initial guess in gams to
[2.515002447346428749 ;-1.687784592789972171 ;-1.119446048550189809]
and see whether gams also confirms your MATLAB solution.
syms x y z
errX = 10;
errF = 10;
imax = 25;
TolX = 1e-8;
TolF = 1e-8;
f = [ x^2+x-y^2+x*y+z^2-3
5*(y^2)+y+y*z-x^2+z-7
x+y+z+y*z-z^3-3];
J = jacobian(f,[x,y,z]);
Jinv = inv(J);
xi = [1.253;1.166;0.278] ;
i = 0;
while (errX > TolX || errF > TolF) && i < imax % check the condition
fi = double(subs(f,[x y z],[xi(1) xi(2) xi(3)]));
Ji = double(subs(Jinv,[x y z],[xi(1) xi(2) xi(3)]));
xip1 = xi - Ji*fi;
i = i + 1;
errX = max(abs(xip1-xi))
errF = norm(fi)
fprintf('Iteration %d:\n',i);
fprintf(' x=%.18f\n',xi)
fprintf(' f=%.18f\n',fi)
xi = xip1;
end
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