Achieving Performance With Extended Eigensolver Routines

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 7/13/2023

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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 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.

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

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

Notice revision #20201201

Parent topic: Extended Eigensolver Functionality

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Achieving Performance With Extended Eigensolver Routines