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# EPSLYAPII

EPSLYAPII = “lyapii” - The Lyapunov inverse iteration.

## Notes

This solver implements the method of Lyapunov inverse iteration [Elman and Wu, 2013, Meerbergen and Spence, 2010] to compute rightmost eigenvalues of non-Hermitian matrices (or matrix pencils).

At each step of the eigensolver, a Lyapunov equation must be solved, and this is done with an `LME` object, see `EPSLyapIIGetLME()`.

This solver may be useful for analyzing the stability of PDE’s. Note that the method requires the input matrix to be stable, so it generally requires to shift the matrix before passing it in `EPSSetOperators()`.

## References

[Elm13]

H. Elman and M. Wu. Lyapunov inverse iteration for computing a few rightmost eigenvalues of large generalized eigenvalue problems. SIAM J. Matrix Anal. Appl., 34(4):1685–1707, 2013. doi:10.1137/120897468.

[Mee10]

K. Meerbergen and A. Spence. Inverse iteration for purely imaginary eigenvalues with application to the detection of Hopf bifurcations in large-scale problems. SIAM J. Matrix Anal. Appl., 31(4):1982–1999, 2010. doi:10.1137/080742890.

## See Also

EPS: Eigenvalue Problem Solver, `EPS`, `EPSType`, `EPSSetType()`, `EPSLyapIIGetLME()`, `EPSSetOperators()`

## Level

beginner

## Location

src/eps/impls/lyapii/lyapii.c

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