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Valentin Albillo · 03-05-2021, 06:21 PM

Hi, all:

I've just made available Update #26 at my HP site, namely the following 8 files (this makes 609 files in all which you can see and/or download for free):

Note: I'll appreciate it if very much if you would please refrain from posting anything to this thread, so that it only contains the update announcements and listings themselves and nothing else. If you want to comment something please create another thread or PM me for any questions or comments you want addressed. Thanks.

2021-03-05:   Update #26   (8 files, including one new Article):

       HP Article VA042b - Boldly Going - Outsmarting PROOT (71B).pdf  (click to see or download)  in Section HP Calculator Articles

15-page article belonging to my "Boldly Going" series, this is the original version for the HP-71B of my article "HP Article VA042a - Boldly Going - Outsmarting PROOT (42S)".

Though this article appears at first sight quite similar to the version for the HP-42S published in Update #24, it was actually written earlier and includes additional sections discussing the internal workings of PROOT and their differences, as well as more examples specific to the 12-digit precision available in the HP-71B, which aren't featured in the HP-42S version. Also, it can be very useful for HP-42S users to better understand the RPN version innards, as the BASIC code is much clearer and the algorithm is exactly the same.

The article includes a small 11-line BASIC subprogram PZER (plus an optional driver) for the HP-71B and emulators (Emu71/DOS, Emu71/Win, go71b, etc.) dealing with a glaring limitation of the HP-71B Math ROM’s keyword PROOT, the polynomial root finder which finds at once all real/complex roots of an N^th-degree polynomial but only works for polynomials having real coefficients. On the other hand, PZER works efficiently and accurately for polynomials whose coefficients are real and/or complex, and can work globally (no user inputs or initial guesses required whatsoever, just the coefficients) while also providing the user with extra control if desired. It can be called from your own programs or manually from the command line.

The article features tables detailing timings and relative speeds for the various devices physical and virtual, plus 10 fully worked examples, including one comparing PZER's performance vs. PROOT when finding all 100 complex roots of a 100^th-degree polynomial (200 components in all) to 12-digit accuracy. There's also examples solving polynomials having multiple roots (double, triple, ...) and exploring how to use the options to enhance their accuracy.

Last but not least, there's also the following files (click on any of them to see or download):

3 Selected HP and SHARP Threads:

      HP Thread VA043 - 2004-06-15 - Geometric progression.pdf
      HP Thread VA044 - 2004-06-25 - A simple question on trading.pdf
      SHARP Thread VA004b - 2003-12-02 - How many calcs do you have.pdf

4 Selected FractVal images:

      Misc Picture VA009 - Sample - Cosmic Panspermia - VF171204AE.jpg
      Misc Picture VA217 - Pulsar Overload - VF171205AZ.jpg
      Misc Picture VA257 - Avocado Still Life - VF170626AA.jpg
      Misc Picture VA278 - Fractal Op-Art - VF161220AS.jpg
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I'll appreciate it if very much if you would please refrain from posting anything to this thread, so that it only contains the update announcements and listings themselves and nothing else. If you want to comment something please create another thread or PM me for any questions or comments you want addressed. Thanks.

V.