If you only tabulate ArcTanh(BP) then you would still need to compute the Tanh of that to get your BP which is needed for the other terms, and also state updates.
I have tried similar things in the past, but they didn't work that well for me. It was always the "bendy bits" of the approximations which needed the most help, and in that case unless you've got a really good approximation the first NR refinement could possibly go wrong and you're in an as bad if not worse position since you've just blown you cache doing the table lookup! I should probably look at it again though just to make sure.mystran wrote: ↑Thu Feb 27, 2020 7:14 am On second thought though, rather than tabulating atanh(BP) directly, you could tabulate a fully converged linearisation. The potential advantage is that if the tabulated result is slightly inaccurate (ie. we don't quite hit the linearisation point, but fairly close to it), then this might allow for a reduced error.
In fact, this leads to the approach I've been suggesting (in PMs at least) in the past as well. While I still haven't tried this in practice yet, in theory you could always add extra dimensions for each of the non-linearities (which you probably should be doing with NR as well), factor the system (eg. using LU) until you only have the non-linear sub-block left (same as with Newton), but then rather than iterating until convergence, fetch either the direct result or the fully converged linearisation for the whole non-linear block from a pre-computed MIMO table.
Additionally, if the table lookup is used simply as a short-cut for NR, then it becomes straight-forward to throw in an extra NR iteration or two to further refine the results if desired. This could allow for a lower resolution table, while still avoiding the pathological cases with NR by always providing a good initial guess that (hopefully) guarantees quadratic converge straight away.
In any case, most of this is just random thoughts really.
