# [petsc-dev] Symmetry acceleration of the Jacobi-Davidson method (in SLEPc)

Krzysztof Gawarecki dkg2140 at gmail.com
Fri Feb 13 08:06:38 CST 2015

```Dear All,

I'm calculating eigenvalues and eigenvectors of the matrix which has
specific kind of symmetry.
Due to this symmetry I obtain the eigenvalues which are doubly degenerated.
So eg. eigeinvalue 'e1' has eigenvectors 'a1' and 'b1'. These eigenvectors
are related to each other by the relation a1 = T b1, where T is a matrix
(given for my problem).
So it is enough to calculate only one eigenvector for each eigenvalue (and
the second one can be calculated by matvec operation). This situation has
been described in http://dl.acm.org/citation.cfm?id=2494747.

How could I take advantage on this in EPSSolve in Jacobi-Davidson method?
Could I add two vectors to the subspace (the second one would be calculated
by multiplying the first one by matrix T) in every iteration? Should I
modify function "dvd_updateV_update_gen" in dvd_updatev.c ?

I would be very grateful for any suggestion.

Krzysztof
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