Version 1.4.0

12th April 2013

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HSL_EA19 Sparse symmetric or Hermitian: leftmost eigenpairs

HSL_EA19 uses a subspace iteration method to compute the leftmost eigenvalues and corresponding eigenvectors of a real symmetric (or Hermitian) operator A acting in the n-dimensional real (or complex) Euclidean space Rn, or, more generally, of the problem

Ax = λBx,

where B a real symmetric (or Hermitian) positive-definite operator. By applying HSL_EA19 to A, the user can compute the rightmost eigenvalues of A and the corresponding eigenvectors. HSL_EA19 does not perform factorizations of A or B and thus is suitable for solving large-scale problems for which a sparse direct solver for factorizing A or B is either not available or is too expensive.

The convergence may be accelerated by the provision of a symmetric positive-definite operator T that approximates the inverse of (A σB) for a value of σ 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.