Looking for TVM contributions

[robve]

I've expanded the comparisons by including another Newton method. The following results compare Newton and Hybrid to another Newton solver that was mentioned on the HP Forums before. To ensure fairness, I used the exact same initial i% guess that performs very well thanks to Albert and I've used the same termination condition for all four methods compared. To emulate BEGIN mode I added PV+=PMT and FV-=PMT to solve rate i% with this other Newton solver (PV and FV updates are undone to compute FVerror.)

  tvmperfcomp-voidware-newton-hybrid.pdf (Size: 36.22 KB / Downloads: 3)

This other Newton solver performs objectively worse than the Newton and Hybrid methods used and discussed in this thread. There is one minor benefit of this method. When we disregard the problematic case that requires as many as 53 evaluations to converge (!), this Newton method requires slightly fewer evaluations on average. However, the results are less accurate and some are wrong. Perhaps interesting to note is that additional iterations (with g=1 to continue with one retry) may improve the results in some cases, but mostly harms the result. Interestingly, this is the opposite of the Newton method used and discussed in this thread. I suppose this aligns with the claims that Newton should not need continuation theoretically after the termination condition was met, but depending on the choice of f and f' expressions may benefit from additional iterations.

- Rob