> El 9 jul 2018, a las 12:23, Gard Spreemann <[email protected]> escribió:
>
> 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.
It is a Krylov solver based on the Krylov subspace generated by A and vector v,
so only matrix-vector products with A are computed. The polynomial is
explicitly built only on the reduced matrix T, not A.
Jose
>
> Best,
> Gard
