f1=@(x) 2*x(1)+2*x(2)+0.03*sin(x(1)+x(2))-4;
f2=@(x) 5*x(1)+7*x(2)+0.07*cos(x(1)-x(2))-8;
df1dx1=@(x) 2+0.03*cos(x(1)+x(2));
df1dx2=@(x) 2+0.03*cos(x(1)+x(2));
df2dx1=@(x) 5-0.07*sin(x(1)-x(2));
df2dx2=@(x) 7+0.07*sin(x(1)-x(2));

x0=[4 8];
di=[df1dx1(x0)-1 df1dx2(x0);df2dx1(x0) df2dx2(x0)-1];
d=[df1dx1(x0) df1dx2(x0);df2dx1(x0) df2dx2(x0)];
ii=[1 0; 0 1];
a=inv(di)*d;

i=1;
while(i<20)
y=(ii-a)*[f1(x0) ; f2(x0)]+a*(x0');
dist=((x0(1)-(y')(1))^2+(x0(2)-(y')(2))^2)^0.5;
if(dist<10^-15)
printf('%.15d \n %.15d',x0(1),x0(2));
break
end
printf('fails %d th\n',i);
i=i+1;

x0=y';
end