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Polynomial Interpolation for HP-67
05-11-2022, 05:31 AM
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RE: Polynomial Interpolation for HP-67
(05-11-2022 01:04 AM)Matt Agajanian Wrote:  Does anyone have an HP-67 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 HP-67, HP-25 and HP-15C.
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 HP-67 even though some of the commands that access the stack registers are missing.

(05-11-2022 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:
(03-09-2019 04:49 PM)Thomas Klemm Wrote:  Example:

Find a quadratic polynomial given these 3 points: \(P_0(-5, 12)\), \(P_1(1, 13)\) and \(P_2(2, 11)\)

0 STO 00

-5 ENTER 12
XEQ "P+"

1 ENTER 13
XEQ "P+"

2 ENTER 11
XEQ "P+"


These are the coefficients of the Newton polynomial:

R03: 12.000000
R05:  0.166667
R07: -0.309524

This leads to the formula:

\(f(x) = 12 + (x+5)(\frac{1}{6} - (x-1)\frac{13}{42})\)

But you can expand it to get:

\(
-\frac{13 x^2}{42} - \frac{15 x}{14} + \frac{302}{21}
\)
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RE: Polynomial Interpolation for HP-67 - Thomas Klemm - 05-11-2022 05:31 AM



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