12th April 2013
HSL_EA19 uses a subspace iteration method to compute the leftmost eigenvalues and corresponding eigenvectors of a real symmetric (or Hermitian) operator acting in the -dimensional real (or complex) Euclidean space , or, more generally, of the problem
where a real symmetric (or Hermitian) positive-deﬁnite operator. By applying HSL_EA19 to , the user can compute the rightmost eigenvalues of and the corresponding eigenvectors. HSL_EA19 does not perform factorizations of or and thus is suitable for solving large-scale problems for which a sparse direct solver for factorizing or is either not available or is too expensive.
The convergence may be accelerated by the provision of a symmetric positive-deﬁnite operator that approximates the inverse of for a value of that does not exceed the leftmost eigenvalue. Computation time may also be reduced by supplying vectors that are good approximations to some of the eigenvectors.