How do I reiterate a set of equations in Matlab until convergence?

Question

I have three equations, where u is previously defined as an mx1 vector and A is an mxn matrix:

v = A'*u/norm(A'*u);
s = norm(A*v);
u = A*v/norm(A*v);

I'm trying to reiterate these equations until they converge. I've been trying to use the solve() function:

[v s u] = solve(v == A'*u/norm(A'*u), s == norm(A*v), u == A*v/norm(A*v), v, s, u)

But I keep getting a whole bunch of errors when using that. How else could I do this?

Answer 1

Not sure what you were expecting using solve, but you can do this numerically using a while loop until the change in v and u is smaller than some tolerance.

A=rand(5,4); %// sample data
u=rand(5,1);
u2=u+1;v2=1;v=0; %// to make sure we enter the loop
tol=1e-11 %// tolerance on change in u or v, to exit loop
while(norm(u2-u)>tol && norm(v2-v)>tol) %// continue until both changes are small enough
    u2 = u;
    v2 = v;
    v = A'*u/norm(A'*u) %// calculate new value of v
    s = norm(A*v);
    u = A*v/norm(A*v) %// new value of u
end