INEXACT INVERSE SUBSPACE ITERATION WITH PRECONDITIONING APPLIED TO NON-HERMITIAN EIGENVALUE PROBLEMS

摘要

Convergence results are provided for inexact inverse subspace iteration applied tothe problem of finding the invariant subspace associated with a small number of eigenvalues ofa large sparse matrix. These results are illustrated by the use of block-GMRES as the iterativesolver. The costs of the inexact solves are measured by the number of inner iterations needed by theiterative solver at each outer step of the algorithm. It is shown that for a decreasing tolerance thenumber of inner iterations should not increase as the outer iteration proceeds, but it may increase forpreconditioned iterative solves. However, it is also shown that an appropriate small rank change tothe preconditioner can produce significant savings in costs and, in particular, can produce a situationwhere there is no increase in the costs of the iterative solves even though the solve tolerances arereducing. Numerical examples are provided to illustrate the theory.