NEPRII

NEPRII = “rii” - Simple residual inverse iteration with varying shift.

Notes

This is the default solver, although it is very basic. Users are advised to try other solvers.

This solver is based on the modification proposed by Neumaier [1985] of the classical residual inverse iteration method. At each step, this method has to solve a system of linear equations. Call NEPRIIGetKSP() to configure the KSP object used for this. When using iterative linear solvers, the preconditioner will be updated in each step or not, depending on NEPRIISetLagPreconditioner(), and the tolerance will be constant or not depending on NEPRIISetConstCorrectionTol().

The solver incorporates deflation, so that several eigenpairs con be computed. Details of the implementation in SLEPc can be found in [Campos and Roman, 2021].

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.

[Neu85]

A. Neumaier. Residual inverse iteration for the nonlinear eigenvalue problem. SIAM J. Numer. Anal., 22(5):914–923, 1985. doi:10.1137/0722055.

See Also

NEP: Nonlinear Eigenvalue Problems, NEP, NEPType, NEPSetType(), NEPRIIGetKSP(), NEPRIISetLagPreconditioner(), NEPRIISetConstCorrectionTol()

Level

beginner

Location

src/nep/impls/rii/rii.c

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