Lagrange interpolation and partial fraction decomposition

Revision en1, by adamant, 2021-12-27 02:35:01

Hi everyone!

Today I'd like to write yet another blog about polynomials. It's quite well-known that the system

$$$\begin{gather}P(x_0) = y_0, \\ P(x_1) = y_1, \\ \dots \\ P(x_n) = y_n\end{gather}$$$

has a unique solution $$$P(x)$$$ among polynomials of degree at most $$$n$$$. One of direct ways to prove that such a polynomial exists is through Lagrange's interpolation. To have a better grasp of it, let's recall that $

Tags polynomial interpolation, lagrange-interpolation, chinese remainder theo., crt, polynomials, partial fraction

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en11 English adamant 2021-12-28 14:17:03 1113 extra about switching from x^k to (x+a)^k
en10 English adamant 2021-12-28 00:19:18 13 cut
en9 English adamant 2021-12-27 23:59:16 44
en8 English adamant 2021-12-27 23:57:40 7
en7 English adamant 2021-12-27 23:55:41 234
en6 English adamant 2021-12-27 23:52:54 1150 (published)
en5 English adamant 2021-12-27 19:00:47 541
en4 English adamant 2021-12-27 17:05:24 2
en3 English adamant 2021-12-27 17:04:17 2638
en2 English adamant 2021-12-27 14:45:47 555
en1 English adamant 2021-12-27 02:35:01 477 Initial revision (saved to drafts)