Newton's theorem with respect to a lot of centers and their applications

✍ Scribed by Gui Zuhua

• Publisher: Springer
• Year: 1996
• Tongue: English
• Weight: 172 KB
• Volume: 17
• Category: Article
• ISSN: 0253-4827
• DOI: 10.1007/bf00123109

✦ Synopsis

In this paper we shall extend the paper [l] to a separateTaylor's Theorem with respect to a lot of centers, namely Newton's Theorem of a lot of centers. From it we obtain the analogous results in the paper [2], namely an .interpolation formula of the difference of higher order. Finally we give their applications.

Key words Newton's interpolation formula, Newton's polynomial of a lot of centers, Newton's Theorem of a lot of centers, interpolation formula of the difference of higher order

I. Simple Statement about Newton's Interpolation Formula

We write xl~-----xl+kll (k>~O) and also may define the condition ofk~0.

We define Ah/(x) =f(x+ll) - [(x') here !, is a divided distance of the first order difference. We define )=t(x+kl,) -cl/(x+(k-+... A~l/(x)-'Ah +(--1)~C|/(x.-l-(k-i)ll)+..,+( -1)*f(x)