% lanczos.m - Simple Lanczos iteration for symmetric matrix  A .
 
  function e = lanczos(A,nsteps);
  N = length(A);
  qold = zeros(N,1);
  b = randn(N,1); q = b/norm(b);
  a = []; c = 0;
  for n = 1:nsteps
     v = A*q;
     a = [a; q'*v];
     v = v - c(n)*qold - a(n)*q;
     c = [c; norm(v)];
     qold = q;
     q = v/c(n+1);
  end
  c = c(2:n);
  T = diag(a) + diag(c,-1) + diag(c,1);
  e = sort(eig(T));