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# PEPJD

PEPJD = “jd” - The Jacobi-Davidson method for polynomial eigenproblems.

## Notes

This is a preconditioned eigensolver, that is, it may be competitive when computing interior eigenvalues in case the shift-and-invert spectral transformation is too costly and a good preconditioner is available.

The implemented method is polynomial Jacobi-Davidson [Sleijpen et al., 1996]. It is possible to set several options of the algorithm, such as the restart (`PEPJDSetRestart()`) or the fix parameter (`PEPJDSetFix()`). The details of the SLEPc implementation are in [Campos and Roman, 2020].

The preconditioner is specified via the internal `ST` object and its associated `KSP`. The preconditioner will be recomputed whenever the shift is updated, unless this is disabled with `PEPJDSetReusePreconditioner()`.

## References

[Cam20a]

C. Campos and J. E. Roman. A polynomial Jacobi-Davidson solver with support for non-monomial bases and deflation. BIT, 60(2):295–318, 2020. doi:10.1007/s10543-019-00778-z.

[Sle96]

G. L. G. Sleijpen, A. G. L. Booten, D. R. Fokkema, and H. A. van der Vorst. Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT, 36(3):595–633, 1996. doi:10.1007/bf01731936.

## See Also

PEP: Polynomial Eigenvalue Problems, `PEP`, `PEPType`, `PEPSetType()`, `PEPGetST()`, `PEPJDSetRestart()`, `PEPJDSetFix()`, `PEPJDSetReusePreconditioner()`

## Level

beginner

## Location

src/pep/impls/jd/pjd.c

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