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# EPSPOWER

EPSPOWER = “power” - The simple power iteration and inverse iteration.

## Notes

This solver is very basic and is not recommended in general, since it will not be competitive with respect to other solvers.

The implemented method is the power iteration, or inverse iteration in case the selected spectral transformation is `STSINVERT`. In this latter case it is possible to use a dynamic shift, as in the RQI method, see `EPSPowerSetShiftType()`.

The solver incorporates deflation so that several eigenpairs can be computed. There is also a two-sided implementation that also computes left eigenvectors.

This solver can also be used for nonlinear inverse iteration on the problem \(A(x)x=\lambda B(x)x\), where \(A\) and \(B\) are not constant matrices but depend on the eigenvector \(x\). This mode is enabled with `EPSPowerSetNonlinear()`. Note that this is a nonlinear eigenvector problem, as opposed to problems addressed in `NEP` that are nonlinear with respect to the eigenvalue.

## See Also

EPS: Eigenvalue Problem Solver, `EPS`, `EPSType`, `EPSSetType()`, `EPSSetTwoSided()`, `EPSPowerSetShiftType()`, `EPSPowerSetNonlinear()`

## Level

beginner

## Location

src/eps/impls/power/power.c

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