Xu

My bad. Perhaps my Matlab version (2007) is too old.

Work for relatively large n? I tried n=9, but Matlab is down.

Here are my codes:

delta=[-1 1 -1 1 -1];
F=[delta(1)*(cos(x5)+cos(2*x5+x1)+cos(3*x5+x2)+cos(4*x5+x3)+cos(5*x5+x4)) - delta(2)*(cos(x6)+cos(2*x6+x1)+cos(3*x6+x2)+cos(4*x6+x3)+cos(5*x6+x4));
delta(2)*(cos(x6)+cos(2*x6+x1)+cos(3*x6+x2)+cos(4*x6+x3)+cos(5*x6+x4)) - delta(3)*(cos(x7)+cos(2*x7+x1)+cos(3*x7+x2)+cos(4*x7+x3)+cos(5*x7+x4));
delta(3)*(cos(x7)+cos(2*x7+x1)+cos(3*x7+x2)+cos(4*x7+x3)+cos(5*x7+x4)) - delta(4)*(cos(x8)+cos(2*x8+x1)+cos(3*x8+x2)+cos(4*x8+x3)+cos(5*x8+x4));
delta(4)*(cos(x8)+cos(2*x8+x1)+cos(3*x8+x2)+cos(4*x8+x3)+cos(5*x8+x4)) - delta(5)*(cos(x9)+cos(2*x9+x1)+cos(3*x9+x2)+cos(4*x9+x3)+cos(5*x9+x4));
-sin(x5)-2*sin(2*x5+x1)-3*sin(3*x5+x2)-4*sin(4*x5+x3)-5*sin(5*x5+x4);
-sin(x6)-2*sin(2*x6+x1)-3*sin(3*x6+x2)-4*sin(4*x6+x3)-5*sin(5*x6+x4);
-sin(x7)-2*sin(2*x7+x1)-3*sin(3*x7+x2)-4*sin(4*x7+x3)-5*sin(5*x7+x4);
-sin(x8)-2*sin(2*x8+x1)-3*sin(3*x8+x2)-4*sin(4*x8+x3)-5*sin(5*x8+x4);
-sin(x9)-2*sin(2*x9+x1)-3*sin(3*x9+x2)-4*sin(4*x9+x3)-5*sin(5*x9+x4);
];
tolerance = .01;
initial_est = ones(1,9);
solution = newton_n_dim(tolerance,initial_est,[x1,x2,x3,x4,x5,x6,x7,x8,x9],F);

All functions are sin/cos.... Cannot get a solution.