On Convergence Rates of Root-Seeking Methods

[brickviking]

(01-31-2017 01:26 PM)RMollov Wrote:  Hi Namir,
I really appreciate your input in this forum, but is this really a home for such topics?

Of course! It includes mathematics, experimentation and just plain old science.

(01-31-2017 01:26 PM)RMollov Wrote:  IMHO solvers in hp calculators do whatever they are supposed to and I don't see room for improvement here given the fact those calculators are no longer made and hardly used.

While I agree for original calculators with no real expandability, for the later generations (HP41–50G) you could create modules/libraries/programs with better functions to supplement the existing ones. I've already seen this in play with my HP50G, and even seen a Gamma function implemented for the Casio 9750G+, and I'm sure you've seen the HP41CL project. As a previous poster has already asserted, nothing's stopping future developments in HP calculator space.

(01-31-2017 01:26 PM)RMollov Wrote:  I for one have used them to get something done and never cared about how it's done internally at low level. Even if I did I don't think I could change anything.

Understanding the limits of what a venerable HP28C can do will make you aware how far you can push some calculations before you eventually have to give up and step up to "big iron". I've been intrigued about internal calculator functions and their limits since I first discovered that the HP-34C could calculate the Gamma function. I'd never seen another calculator do that. At the time I called it non-integer primes, but since discovered its proper name. I was fascinated that I could put in 3.1415 into n! and actually get a result.

I also investigate accuracy for the calculators that I have; it's fun to know some of the limits of what a calculator can do. I grant that yes, they're there to pick up and use without worrying about the nuts-and-bolts (or we'd all be writing our own WP43Q on a Raspberry Pi with a LCD display with an embedded Smalltalk), but it's interesting to realise that earlier calculators were only a couple of magnitudes better than a really good sliderule operator. Programmability and "modern" methods of manufacture changed the game in this, I reckon.

(Post 53, after a long hiatus of post counters)
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Cheers, BrickViking (a.k.a. DrSmokey)