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# PEPSTOAR

PEPSTOAR = “stoar” - A symmetric variant of TOAR.

## Notes

This solver is available for quadratic eigenproblems only.

It is an alternative to `PEPTOAR` in the case of `PEP_HERMITIAN` problems. It tries to exploit the symmetry of the matrices by working with a special linearization where the matrices are Hermitian. However, this pencil in indefinite, so it uses a pseudo-Lanczos recurrence that may become numerically unstable. The method is described in [Campos and Roman, 2016].

The solver incorporates support for interval computation with `PEPSetInterval()`. Then it will proceed with a spectrum slicing scheme as described in [Campos and Roman, 2020]. This is particularly useful in the case of `PEP_HYPERBOLIC` problems.

## References

[Cam16c]

C. Campos and J. E. Roman. Restarted Q-Arnoldi-type methods exploiting symmetry in quadratic eigenvalue problems. BIT, 56(4):1213–1236, 2016. doi:10.1007/s10543-016-0601-5.

[Cam20b]

C. Campos and J. E. Roman. Inertia-based spectrum slicing for symmetric quadratic eigenvalue problems. Numer. Linear Algebra Appl., 27(4):e2293, 2020. doi:10.1002/nla.2293.

## See Also

PEP: Polynomial Eigenvalue Problems, `PEP`, `PEPType`, `PEPSetType()`

## Level

beginner

## Location

src/pep/impls/krylov/stoar/stoar.c

## Implementations

PEPSTOAR_QSlice() in src/pep/impls/krylov/stoar/qslice.c

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