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# 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

Index of all NEP routines Table of Contents for all manual pages Index of all manual pages