GMRES Algebra

Hi. GMRES has a lot of variations. Especially when it comes to ways to parallelize it. dgmres, fibGMRES, etc.. This paper is an attempt to generalize and denote how you could reorganize the order of computations in any GMRES algebra to be equivalent to the order of computations in a simple polynomial evaluation problem. The point is that this simpler polynomial evaluation problem kind of made it apparent why you might not have a lot of hope in pipelining GMRES, and why methods like fibGMRES might be the best you can hope for.

I don't have enough knowledge to be able to know if I'm doing the abstract algebra correctly. So, I apologize if it's terribly wrong. Nonetheless, it's the one work of mine that I'm the proudest of, which is all the more depressing for why whenever I bring it up, I'm only ever more apparent of how much of a crank I really am. Please talk to me.

2016 Work
  • Writeup (pdf warning)