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 Ne = 8 or at most using Ne = 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 Ne, 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, Ne = 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.

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Notice revision #20110804

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