I'm Cristiano Dorigo, a bachelor graduated student in Applied Mathematics in Verona, Italy, and now I'm a student of Master Degree in Mathematics in the University of Verona.

I was selected as partecipant student for the SOCIS 2016 under GNU Octave for the project "Improve iterative methods for sparse linear systems".

The idea of this project is at first to improve the methods actually implemented in Octave to solve linear systems as gmres, pcg, bicg, bicgstab, qmr, pcr. Ideed these algorithms have, for example, a similar structure in the initial part (where the inputs are checked). Other possible improvement can be the synchronization of their error messages or to check the documentation. Another critical point is to check the compatibility of the results with Matlab, i.e. to check, for example, if the quality of the solution with the same method is equal both in Matlab and Octave, to see if they use the same number of iterations, same residual,...

The second step is to implement, as much as possible, some iterative methods that, for example, are in Matlab, but not in Octave. The suggested methods are minres, symmlq, tfqmr, bicgstabl, lsqr. The order of the implementation can be decided with the mentors giving priority to the useful or the necessary ones.

**Timeline:**

I think to split the work in the same two step mentioned before, i.e. improvements and implementation.

- The first two weeks I want to study the methods already implemented but that I haven't faced off during my student career, i.e. bicg, bicgstab, qmr and pcr and to study their codes.
- The second two/three weeks I want at first to consult the mentors to decide where and how to improve these methods, then to apply these ideas.
- The remaining time will be spent to implement the new methods. I want to implement these methods one by one, after a discussion with the mentors about which methods have priority.

The reference book is "Iterative Methods for sparse linear systems" 2-nd Edition by Yousef Saad, which is available here www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf

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