Polynomial interpolation when value of Xs are hidden

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Aydin
Posts: 1
Joined: Mon May 26, 2014 12:29 pm UTC

Polynomial interpolation when value of Xs are hidden

I need to know when the value of Xs and coefficients are hidden and the value of Ys are available:

1) Can anybody recover the unique polynomial if he has all values of Ys, to obtain the constant value?

2) What if he has more Ys values evaluated on different polynomials. So all polynomials have same constant value and we interpolate same range of Xs for each of them to obtain Ys values, but their coefficients are different.

alessandro95
Posts: 109
Joined: Wed Apr 24, 2013 1:33 am UTC

Re: Polynomial interpolation when value of Xs are hidden

I don't understand which informations exactly do you have, you have a polynomial axn+a1xn-1....+an-1x+an passing througth a set of points {(xn,yn)}, what exactly do you know? only the various yn?
The primary reason Bourbaki stopped writing books was the realization that Lang was one single person.

mike-l
Posts: 2758
Joined: Tue Sep 04, 2007 2:16 am UTC

Re: Polynomial interpolation when value of Xs are hidden

I think you're asking to recover a polynomial from its range? This is impossible over the reals (eg all odd degree polynomials have range equal to the whole real line). Working over other domains you can probably do some more. For example if you happen to know your polynomial is linear and your domain has two points, the range narrows the initial polynomial down to two possibilities. You'd need to be more specific on exactly what information you have
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