Andrew Knyazev UC Denver 	

Abstract.
Block Locally Optimal Preconditioned Eigenvalue Xolvers (BLOPEX) is a package, written in C, that at present includes only one eigenxolver, Locally Optimal Block Preconditioned Conjugate Gradient Method (LOBPCG). BLOPEX supports parallel computations through an abstract layer. BLOPEX is incorporated in the HYPRE package from LLNL and is availabe as an external block to the PETSc package from ANL as well as a stand-alone serial library.

Main LOBPCG features: a matrix-free iterative method for computing several extreme eigenpairs of symmetric positive generalized eigenproblems; a user-defined preconditioner; robustness with respect to random initial approximations, variable preconditioners, and ill-conditioning of the stiffness matrix; apparently optimal convergence speed. Numerical comparisons suggest that LOBPCG may be a genuine block analog for eigenproblems of the standard preconditioned conjugate gradient method for symmetric linear systems.