Equation solvers, HP 41CV etc.

[Thomas Okken]

(12-03-2017 05:39 PM)Dieter Wrote:  I wonder if the HP Solve algorithm (or the Integrate code, for that matter) has ever been published.

There is an HP Journal article by William Kahan (don't remember the exact reference, but it's in the MoHPC document set) where he explains some aspects of the algorithm, but the complete algorithm or source code have never been published, as far as I'm aware. I would have loved to use that algorithm in Free42! However, you can suss out a thing or two by giving it a pathological function, say, y=2, or y=x^2+1, and then observing the successive guesses it comes up with.

(I ended up taking some inspiration from HP solve on the 42S, in how to deal with unhelpful starting guesses, and used a combination of bisection, secant method, and Ridders' method, for root refinement. It's fairly close to the 42S solve in terms of convergence, but there's still room for improvement, in terms of convergence, and in terms of handling pathological cases.)