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# EPS_POWER_SHIFT_RAYLEIGH

The power iteration will use a variable shift computed with the Rayleigh quotient.

## Notes

Together with `STSINVERT`, the `EPSPOWER` solver implements the inverse iteration method, i.e., it will apply \((A-\sigma I)^{-1}\) at each iteration, by solving a linear system. With this strategy, the value of the shift will be updated at each iteration as \(\sigma=\frac{x^*Ax}{x^*x}\), where \(x\) is the current eigenvector approximation. The resulting iteration is the RQI method.

Updating the shift may involve a high computational cost if the linear solve is done via a factorization.

Details of the three variants can be found in [Hernandez et al., 2005].

## References

[Her05]

V. Hernandez, J. E. Roman, A. Tomas, and V. Vidal. Single vector iteration methods in SLEPc. Technical Report STR-2, Universitat Politècnica de València, 2005. URL: https://slepc.upv.es/documentation.

## See Also

EPS: Eigenvalue Problem Solver, `EPSPowerShiftType`, `EPSPowerSetShiftType()`, `STSetShift()`, `EPSSetTarget()`, `EPS_POWER_SHIFT_CONSTANT`, `EPS_POWER_SHIFT_WILKINSON`

## Level

advanced

## Location

include/slepceps.h

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