Achieving Performance With Extended Eigensolver Routines
- the search interval and the size of the subspace(overestimation of the number of eigenvaluesM0Mwithin 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.
- fast convergence with very high accuracy when seeking up to 1000 eigenpairs (in two to four iterations using= 1.5M0M, and= 8 or at most usingNe= 16 contour points);Ne
- an extremely robust approach.
- should be much smaller than the size of the eigenvalue problem, so that the arithmetic complexity depends mainly on the inner system solver (O(M0NM) 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.