Polynomial Interpolation for HP67

05112022, 01:04 AM
(This post was last modified: 05112022 01:06 AM by Matt Agajanian.)
Post: #1




Polynomial Interpolation for HP67
Hi all.
In the Math/Utilities module for the TI58/59, there’s an interpolation program that fits an nth degree polynomial to n+1 data pairs. It then allows for the calculation when an x value is entered. I would have liked to have a version of that program which would also reveal the polynomial coefficients. I no longer have my TI58C nor the module. So, I can’t download and print the program so I could write an HP67 version. Does anyone have an HP67 or even a 29C polynomial fitting/interpolation program so I could add that to my program library? Thanks 

05112022, 05:31 AM
Post: #2




RE: Polynomial Interpolation for HP67
(05112022 01:04 AM)Matt Agajanian Wrote: Does anyone have an HP67 or even a 29C polynomial fitting/interpolation program so I could add that to my program library? In Lagrangian Interpolation you can find some programs for the HP67, HP25 and HP15C. However these are limited to 3 points. In the program of (42S) Newton Polynomial Interpolation the number of points is only limited by memory. Furthermore points can be added if the interpolation is not considered sufficient. It should be possible to rewrite these programs for the HP67 even though some of the commands that access the stack registers are missing. (05112022 01:04 AM)Matt Agajanian Wrote: I would have liked to have a version of that program which would also reveal the polynomial coefficients. It may not be exactly what you want, but you get the coefficients of the Newton polynomial: (03092019 04:49 PM)Thomas Klemm Wrote: Example: But you can expand it to get: \( \frac{13 x^2}{42}  \frac{15 x}{14} + \frac{302}{21} \) 

05112022, 12:16 PM
Post: #3




RE: Polynomial Interpolation for HP67
I have 3 or 4 routines written in CAdjacent languages that you might be able to adapt. They use the Least Squares method (so you can put more than N data points) from Advanced Engineering Mathematics.
I keep reinventing the wheel. 8^) 

05112022, 12:27 PM
Post: #4




RE: Polynomial Interpolation for HP67
(05112022 05:31 AM)Thomas Klemm Wrote: \(f(x) = 12 + (x+5)(\frac{1}{6}  (x1)\frac{13}{42})\) We can do synthetic multiplication, to transform "offset" polynomial to "normal" polynomial. We do it inside out, first (x1), then (x+5) Code: 13/42 1/6 12 Or, we can convert 1 set of polynomial offsets, to another, in 1 shot. see Funny Factorials and Slick Sums We don't see much benefits here, because "normal" polynomial have zero offsets. a(n) x^n + a(n1) x^(n1) + ... = (x0) * (a(n) + (x0) * (a(n1) + ... From offsets (1,5) → (0,0): Code: 13/42 1/6 12 

05112022, 09:37 PM
Post: #5




RE: Polynomial Interpolation for HP67
(05112022 05:31 AM)Thomas Klemm Wrote: It should be possible to rewrite these programs for the HP67 even though some of the commands that access the stack registers are missing. Done. 

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