HP49-50G: MLSV OK for -1E-495, not OK for -1E-496, ROOT OK for both

[Albert Chan]

(01-25-2024 11:08 AM)Gil Wrote:  I have a program and may get a complex number, for which I look for a solution.

The function is x*EXP(x).

Newton's method is not good for solving x*e^x = a, if |x| is big (*)

Instead, we may solve for the tempered version, by taking ln

(x*e^x = a) --> (ln(x) + x = ln(a)) --> (x + ln(x/a) = 0)

HP71B
> a = -1e-496
> x = ln(-a) ! branch -1
> for i=1 to 3 @ x = (1-ln(x/a))/(1+1/x) @ x @ next i
-1149.12898462
-1149.12896563
-1149.12896564

(*) OTTH, if we already have an extremely good guess, good for finishing touch.