speed can be easily increased without sacrificing the small cost per iteration; see, e.g., Lanczos iteration and LOBPCG. Some of the more advanced eigenvalue algorithms can be understood as variations of the power iteration. For instance, the inverse iteration method applies power iteration to the matrix . Other algorithms look at the whole subspace generated by the vectors . This subspace is known as the Krylov subspace. It can be computed by Arnoldi iteration or Lanczos iteration. See also Rayleigh quotient iteration Inverse iteration References Numerical linear algebra Articles with example Python (programming language) code