By applying the Newton Raphson technique solve the following

By applying the Newton Raphson technique, solve the following non linear
expressions in order to determine the values of x and y up to a tolerance of
0.001. Do not iterate more than 4 times.

Solution

clc
clear;
itr=0;
tol=10;
x=1;y=1;
while ( itr<4 && tol>=0.001),
    itr=itr+1;
    f1=2*x^2+y^2-8;
    f2=6*x+2*y^2-5;
    dfd=[4*x 2*y;6 4*y];
    df=[f1;f2];
    d=inv(dfd)*df;
    x=x+d(1);
    y=y+d(2);
    tol=max(abs(d));
end
if tol>=0.0001,
    disp(\'not conversing by this newton method \');
    disp(\'tolerence after 4 iterations\');
    disp(tol);
else
    disp(\'tol\');
    disp(tol);
    disp(\'ieration\')
    disp(\'itr\');
    disp(\'x=\');
    disp(x);
    disp(\'y=\');
    disp(y);
end

result:

not conversing by this newton method
tolerence after 4 iterations
   11.9617