On Friday 6 July 2018 18:46:56 CEST Jose E. Roman wrote: > > > El 6 jul 2018, a las 16:37, Gard Spreemann <[email protected]> > > escribió: > > > > On Friday 6 July 2018 16:18:27 CEST Jose E. Roman wrote: > >> SLEPc's default eigensolver 'krylovschur' does this kind of computation > >> repeatedly, in an outer loop (the restarts) until eigenvalues are > >> converged. If you call EPSSolve() with -eps_max_it 1 to avoid any restarts > >> then you will get something similar to what you want. The computed basis > >> can be retrieved with EPSGetBV(). However, this is not the intended usage, > >> and hence it is not documented. You will have to look at the source code > >> and see what is being computed. > > > > Thank you. I'll have a look and see if I can make sense of it. > > > > I had the impression that it's only possible to set the *maximum* > > dimension of the Krylov subspaces used though. Is that the case? I'd > > need to set the dimensionality exactly. > > The dimension of the Krylov subspace is controlled by means of the ncv > parameter > http://slepc.upv.es/documentation/current/docs/manualpages/EPS/EPSSetDimensions.html
Thanks. That could be a way out then. > >> What do you need this for? > > > > I need to compute some good approximations of (the action of) certain > > polynomials of a matrix (on a vector). Looking around, it seems there > > are some very nice approximations available if one has an orthonormal > > basis for the Krylov subspaces up to power equal to the degree of the > > polynomial in question. > > If you can explicitly compute the coefficients of the polynomial (in the > monomial basis) you could also consider using SLEPc's MFN module, that > computes f(A)*v where f can be a polynomial. Hmm, do these functions actually compute (the matrices involved in) the full polynomial, or do they do some clever approximation? I believe my matrices will often see a lot of sparsity reduction when one takes a large power of them. Best, Gard
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