NEPNLEIGS#

NEPNLEIGS = “nleigs” - The NLEIGS method.

Notes#

This solver implements the NLEIGS method [Güttel et al., 2014], which is based on rational interpolation followed by linearization. In our implementation, the linear eigensolver for the linearization operates with a compressed Krylov basis, as in the TOAR polynomial eigensolver, see the detailed description in [Campos and Roman, 2021].

This method is particularly appropriate for nonlinear problems with singularities. The solver will try to determine the singularities automatically, but the user can also provide them with NEPNLEIGSSetSingularitiesFunction().

By default, the solver performs the static NLEIGS variant, with constant shift given by NEPSetTarget(). But the dynamic variant (rational Krylov) is also available if a list of shifts is given in NEPNLEIGSSetRKShifts().

NEPNLEIGS also implements a two-sided variant for computing left eigenvectors when NEPSetTwoSided() has been set.

Apart from working with the compressed basis, it is also possible to enable the operation with an explicit basis for the linear eigensolver, see NEPNLEIGSSetFullBasis(). This allows using other eigensolvers via an EPS object obtained with NEPNLEIGSGetEPS(). Also, the explicit basis is activated in the two-sided variant.

References#

[Cam21]

C. Campos and J. E. Roman. NEP: a module for the parallel solution of nonlinear eigenvalue problems in SLEPc. ACM Trans. Math. Software, 47(3):23:1–23:29, 2021. doi:10.1145/3447544.

[Gut14]

S. Güttel, R. van Beeumen, K. Meerbergen, and W. Michiels. NLEIGS: a class of fully rational Krylov methods for nonlinear eigenvalue problems. SIAM J. Sci. Comput., 36(6):A2842–A2864, 2014. doi:10.1137/130935045.

Level#

beginner

Location#

src/nep/impls/nleigs/nleigs.c

Implementations#

NEPNLEIGS_RKcontinuation() in src/nep/impls/nleigs/nleigs.c

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