According to this argument, many electronic circuits are minimum phase, and loudspeakers have both minimum-phase and non-minimum-phase effects (with minimum phase characteristics dominant, it is claimed, in the better loudspeakers).
Rooms, alas, have delayed resonances, the epitome of non-minimum-phase.
So what about this... I could in principle correct the speaker minimum-phase effects *perfectly*.
Room effects, I can only broad brush, which may help or harm.
Some of the fancier room EQ systems now measure both speaker and room effects (using gating) and correct the speakers first.
It's not exactly clear what my Tact system does. The description of what it does does not reveal all the technical details, and the system is not open except to the extent that you can edit a target curve. Reviews are mixed but most say it's better to have target curve capability than none, so it's better than most such systems. Most consumer room correction systems have preconfigured target, they are pure black boxes, take it or leave it. Now there are systems which brag about their approaches in more detail, and may have more configuration options than just setting a target curve, but they tend to be really expensive.
There are open source solutions to room correction by EQ, so you can examine or change the algorithm, but the most developed one works with an obsolete Behringer feedback canceller (has lots of parametric EQ's) because it's cheap. It has hum problems, uses semi-pro rather than audiophile line levels, uses a low-ish sample rate. I bought one at close-out, but then was lured in by the much nicer quality Tact hardware. The open source solution auto-programs the old Behringer through it's serial port.
You could say that any-old computer could do the trick. But any-old computer has a noisy power supply, fan, etc., you don't even want one in your listening room.
In principle, given a system with 10 or more parametric EQ's, you can still use the open source software to figure the optimal parameter settings, then just toggle them manually into Tact or DCX crossover.
I have 13 manual parametric EQ's per channel available in the Tact and about the same number additional ones available in the DCX. Not quite the same as the hundreds of poles Tact can use through it's automated room corrector, but enough to do some good or considerable harm.