"... and this is the whole ballgame: ", "jump out immediately", "... and the idea is disarmingly simple", etc etc.

Written by Claude AI. Which is a problem because Claude text is riddled with engagement bait and filler, making it exhausting to read.

The algebraic manipulation that you use to break the dependency seems to be specific to the matrix being Poisson on a finite-difference grid (is that right?). In that case wouldn’t it make more sense to compare against specialized Poisson solvers?

It looks like this analysis extends to the successive over-relaxation (SOR) method. Does it extend to the symmetric successive over-relaxation method?

What language is that, and what does `0.25_dp` mean?

I doubt outside of a few exceptional cases that one is going to do better on CPU-bound problems than a well-written LAPACK implementation built for the architecture you intend to run on.

Maybe pedagogy was the point? I didn’t really get that from the article, maybe some intention was lost by filtering it through AI.

This article might be good but I always get scared when they use AI art for the header bc I wont know if I'm reading AI slop until i've invested a good amount of time into the article so I just avoid it all together.