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# NEPNARNOLDI

NEPNARNOLDI = “narnoldi” - Nonlinear Arnoldi method.

## Notes

This solver implements the N-Arnoldi method [Voss, 2004], a projection method using an expanding subspace formed with the RII iterate vectors. Hence there are similarities with `NEPRII`. Call `NEPNArnoldiGetKSP()` to configure the linear solver, and `NEPNArnoldiSetLagPreconditioner()` to reduce the cost of updating the preconditioner.

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.

[Vos04]

H. Voss. An Arnoldi method for nonlinear eigenvalue problems. BIT, 44(2):387–401, 2004. doi:10.1023/B:BITN.0000039424.56697.8b.

## See Also

NEP: Nonlinear Eigenvalue Problems, `NEP`, `NEPType`, `NEPSetType()`, `NEPNArnoldiGetKSP()`, `NEPNArnoldiSetLagPreconditioner()`

## Level

beginner

## Location

src/nep/impls/narnoldi/narnoldi.c

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