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