First we assume that a Cholesky factorization of is easily obtainable. We then reformulate (5.1) as a standard Hermitian eigenvalue problem with the matrix as described in the previous subsection (5.5), possibly after making positive definite as noted in the introduction (5.2). The power method of §4.3 now takes the following form.

In step (3),
the computation can be executed into three
steps as

Hence, no explicit knowledge of the matrix is needed for the power method. The power method converges under conditions similar to those for the standard HEP.

Susan Blackford 2000-11-20