Finding polynomials from a set of coordinates
03-11-2017, 10:25 AM
Post: #9
 grsbanks Senior Member Posts: 1,219 Joined: Jan 2017
RE: Finding polynomials from a set of coordinates
(03-10-2017 07:39 PM)tdh79 Wrote:  I need to find polynomial functions from a given set of coordinates, does anyone know how to do this with the 50g?

Fitting a polynomial to a set of coordinates can be done by changing your system into a set of linear equations that you then resolve using the Gauss-Jourdain pivot method.

One thing you need to know is that you need n+1 points to fit a polynomial of degree n. Eg. you need 2 points to fit a line (a.x + b = 0), 3 points to fit a quadratic (a.x2 + b.x + c = 0) etc.

Eg. You have the points (-3,1), (1,0) and (2,1).

For the quadratic to fit, all of these points must satisfy the equation, so substituting the coordinates' values of x and y in the equation you end up with something like this:

a.(-3)2 + b.(-3) + c = 1
a.12 + b.1 + c = 0
a.22 + b.2 +c = 1

-- or --

9a -3b +c = 1
a + b + c = 0
4a + 2b + c = 1

That looks suspiciously like a system of 3 linear equations that you can solve directly on the HP 50g. You will then get your values of a, b and c that you can replace in your quadratic equation and hey presto, there's your polynomial that passes through your three points.

The solution to this system is a=1/4, b=1/4 and c=-1/2

If you plot f(x)=(x^2)/4 + x/4 - 1/2 you'll see that the curve passes through all three points.
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 Messages In This Thread Finding polynomials from a set of coordinates - tdh79 - 03-10-2017, 07:39 PM RE: Finding polynomials from a set of coordinates - Han - 03-10-2017, 07:42 PM RE: Finding polynomials from a set of coordinates - Juan14 - 03-10-2017, 08:44 PM RE: Finding polynomials from a set of coordinates - tdh79 - 03-12-2017, 07:56 PM RE: Finding polynomials from a set of coordinates - Han - 03-10-2017, 09:09 PM RE: Finding polynomials from a set of coordinates - tdh79 - 03-10-2017, 09:13 PM RE: Finding polynomials from a set of coordinates - Han - 03-10-2017, 09:18 PM RE: Finding polynomials from a set of coordinates - tdh79 - 03-10-2017, 09:57 PM RE: Finding polynomials from a set of coordinates - SlideRule - 03-11-2017, 12:53 AM RE: Finding polynomials from a set of coordinates - grsbanks - 03-11-2017 10:25 AM RE: Finding polynomials from a set of coordinates - SlideRule - 03-12-2017, 01:49 PM RE: Finding polynomials from a set of coordinates - Csaba Tizedes - 03-12-2017, 05:58 PM RE: Finding polynomials from a set of coordinates - Dieter - 03-12-2017, 06:38 PM RE: Finding polynomials from a set of coordinates - Csaba Tizedes - 03-12-2017, 08:27 PM RE: Finding polynomials from a set of coordinates - Dieter - 03-12-2017, 11:31 PM RE: Finding polynomials from a set of coordinates - Csaba Tizedes - 03-13-2017, 03:00 PM RE: Finding polynomials from a set of coordinates - grsbanks - 03-13-2017, 03:05 PM RE: Finding polynomials from a set of coordinates - Csaba Tizedes - 03-13-2017, 03:37 PM RE: Finding polynomials from a set of coordinates - SlideRule - 03-13-2017, 02:11 AM RE: Finding polynomials from a set of coordinates - SlideRule - 03-14-2017, 02:20 AM RE: Finding polynomials from a set of coordinates - tdh79 - 03-19-2017, 10:35 AM RE: Finding polynomials from a set of coordinates - SlideRule - 03-19-2017, 11:49 PM

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