# [Trilinos-Users] [EXTERNAL] Question about GCRODR in Belos

Parks, Michael L mlparks at sandia.gov
Thu Aug 9 23:28:38 EDT 2018

```Wen,

You can find a better description of the method, including pseudocode for the solver, in the associated paper Recycling Krylov Subspaces for Sequences of Linear Systems at https://epubs.siam.org/doi/abs/10.1137/040607277.

The application of the operator to the recycle space is in general necessary to update the image of that space if the operator has changed from one linear system to the next. (See instructions 2-19 in the pseudocode in the paper.) If the operator has not changed, as in your case, much of this work can be skipped. The GCRODR implementation in Belos assumes the operator may change from one solve to the next, so you would have to modify the solver to avoid this extra work if this is not the case.

Best,

– Mike

---
Michael L. Parks, Ph.D.
Manager, Computational Mathematics Dept.
Center for Computing Research
Sandia National Laboratories
www.sandia.gov/~mlparks<http://www.sandia.gov/~mlparks>

-----Original Message-----
From: Trilinos-Users [mailto:trilinos-users-bounces at trilinos.org] On Behalf Of Wen Yan
Sent: Thursday, August 9, 2018 10:43 AM
To: trilinos-users at trilinos.org
Subject: [EXTERNAL] [Trilinos-Users] Question about GCRODR in Belos

Dear Trilinos users,

I am trying to use GCRODR to solve a sequence of linear systems Ax_i=b_i, where the operator A does not change but the right side b_i slightly changes. The setup of GCRODR works, and the reported number of iterations after the first linear system is reduced compared to cases using PseudoBlockGMRES. However, I found that inside GCRODR->solve() and before the iterations, the operator A is applied to one multi vector with column number equal to the number of recycled vectors. Therefore there is no saving in computational time. I was using default parameters for GCRODR.

I was wondering if this is the expected behavior of GCRODR, or if there is a switch controlling it. I didn’t find that on the document webpage.

Thank you!

Wen Yan

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