41C/CV root finders

[Ángel Martin]

(05-25-2015 07:19 PM)Dieter Wrote:  I think there are some power symbols "^" missing. Both in the derivative and in the initial guess.

You're right - sorry I didn't notice those before, The exponent signs were not handled well in the copy-paste action; I have corrected the expressions in the initial post now.

The initial guess just look intuitively appropriate to me, I confess I didn't derive it from any algorithm or deductive process... but it just looked right - yes I know, math heresy but sometimes one must follow the hunch even in math.

(05-25-2015 07:19 PM)Dieter Wrote:  BTW if space is an issue there is a very simply solution: simply set the inital i to a value very close to zero, e.g. 10^–4. A value of exactly zero will not work because the standard TVM formulas divide by i, but a value very close to this would return (approximately) the estimate I posted - right after the first iteration. So all you lose is a bit of execution speed – i.e. the difference between the time required for one iteration loop and the calculation of the initial estimate. ;-)

I fail to see how reducing the initial guess to a near-zero value will solve the problem when there is not a solution to be found...which is the only problem left. Again, the initial guess I use works rather well for all other *solvable* cases, it's sweet and short to obtain and doesn't require too many iterations to converge.

The SandMath manual has some further details in case it helps.

Thanks Dieter for the suggestions.

'AM