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# EPSCISS

EPSCISS = “ciss” - A contour integral eigensolver based on the Sakurai-Sugiura scheme.

## Notes

This solver is based on the numerical contour integration idea proposed initially by Sakurai and Sugiura [2003] and improved later by adding a Rayleigh-Ritz projection step [Sakurai and Tadano, 2007].

Contour integral methods are able to compute all eigenvalues lying inside a region of the complex plane. Use `EPSGetRG()` to specify the region. However, the computational cost is usually high because multiple linear systems must be solved. For this, we can use the `KSP` object inside `ST`, or several independent `KSP`s, see `EPSCISSSetUseST()`.

Details of the implementation in SLEPc can be found in [Maeda et al., 2016].

## References

[Mae16]

Y. Maeda, T. Sakurai, and J. E. Roman. Contour integral spectrum slicing method in SLEPc. Technical Report STR-11, Universitat Politècnica de València, 2016. URL: https://slepc.upv.es/documentation.

[Sak03]

T. Sakurai and H. Sugiura. A projection method for generalized eigenvalue problems using numerical integration. J. Comput. Appl. Math., 159(1):119–128, 2003. doi:10.1016/S0377-0427(03)00565-X.

[Sak07]

T. Sakurai and H. Tadano. CIRR: a Rayleigh-Ritz type method with contour integral for generalized eigenvalue problems. Hokkaido Math. J., 36(4):745–757, 2007. doi:10.14492/hokmj/1272848031.

## See Also

EPS: Eigenvalue Problem Solver, `EPS`, `EPSType`, `EPSSetType()`, `EPSGetRG()`

## Level

beginner

## Location

src/eps/impls/ciss/ciss.c

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