EPS_POWER_SHIFT_WILKINSON

The power iteration will use a variable shift computed with Wilkinson’s approach.

Note

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 proposed by Wilkinson, see [Parlett, 1980, 8.10].

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.

[Par80]

B. N. Parlett. The Symmetric Eigenvalue Problem. Prentice-Hall, Englewood Cliffs, NJ, 1980. Reissued with revisions by SIAM, Philadelphia, 1998.

See Also

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

Level

advanced

Location

include/slepceps.h

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