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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Answers (2)
VBBV
on 18 Nov 2022
Edited: VBBV
on 18 Nov 2022
fc(:,i+1)=subs(fc,[x;y;z],xn)
jc(:,i+1)=subs(jc,[x;y;z],xn)
3 Comments
VBBV
on 18 Nov 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
on 18 Nov 2022
Edited: Torsten
on 18 Nov 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 Comments
Torsten
on 26 Nov 2022
Edited: Torsten
on 26 Nov 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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