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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
    M
    0
    (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
    M
    0
    = 1.5
    M
    , 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
M
0
, and the number of outer refinement loops to reach the desired accuracy. In practice you should use
M
0
> 1.5
M
,
N
e
= 8
, and at most two refinement loops.
For better performance:
  • M
    0
    should be much smaller than the size of the eigenvalue problem, so that the arithmetic complexity depends mainly on the inner system solver (O(
    N
    M
    ) 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.
Product and Performance Information
Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.
Notice revision #20201201

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.