Achieving Performance With Extended Eigensolver Routines

In order to use the Extended Eigensolver Routines , you need to provide

• the search interval and the size of the subspace M₀ (overestimation of the number of eigenvalues M within a given search interval);

• the system matrix in dense, banded, or sparse CSR format if the Extended Eigensolver predefined interfaces are used, or a high-performance complex direct or iterative system solver and matrix-vector multiplication routine if RCI interfaces are used.

In return, you can expect

• fast convergence with very high accuracy when seeking up to 1000 eigenpairs (in two to four iterations using M₀ = 1.5M, and N_e = 8 or at most using N_e = 16 contour points);

• an extremely robust approach.

The performance of the basic FEAST algorithm depends on a trade-off between the choices of the number of Gauss quadrature points N_e, the size of the subspace M₀, and the number of outer refinement loops to reach the desired accuracy. In practice you should use M₀ > 1.5 M, N_e = 8, and at most two refinement loops.

For better performance:

• M₀ should be much smaller than the size of the eigenvalue problem, so that the arithmetic complexity depends mainly on the inner system solver (O(NM) for narrow-banded or sparse systems).

• Parallel scalability performance depends on the shared memory capabilities of the of the inner system solver.

• For very large sparse and challenging systems, application users should make use of the Extended Eigensolver RCI interfaces with customized highly-efficient iterative systems solvers and preconditioners.

• For the Extended Eigensolver interfaces for banded matrices, the parallel performance scalability is limited.