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# PEPTOAR

PEPTOAR = “toar” - The Two-level Orthogonal Arnoldi method (TOAR) for polynomial eigenvalue problems.

## Notes

This is the default solver, and is recommended in most situations.

It implements the Two-level Orthogonal Arnoldi procedure [Lu et al., 2016], which carries out an implicit linearization and operates with an orthogonal Krylov basis stored in a compact form \(V = (I \otimes U) S\). The details of the SLEPc implementation can be found in [Campos and Roman, 2016].

## References

[Cam16a]

C. Campos and J. E. Roman. Parallel Krylov solvers for the polynomial eigenvalue problem in SLEPc. SIAM J. Sci. Comput., 38(5):S385–S411, 2016. doi:10.1137/15M1022458.

[Lu16]

D. Lu, Y. Su, and Z. Bai. Stability analysis of the two-level orthogonal Arnoldi procedure. SIAM J. Matrix Anal. Appl., 37(1):195–214, 2016. doi:10.1137/151005142.

## See Also

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

## Level

beginner

## Location

src/pep/impls/krylov/toar/ptoar.c

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