Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!tut.cis.ohio-state.edu!ucbvax!VM1.NODAK.EDU!beigel-richard%YALE.ARPA From: beigel-richard%YALE.ARPA@VM1.NODAK.EDU (Richard Beigel) Newsgroups: comp.theory Subject: polynomial interpolation Message-ID: <8912270836.AA24311@thailand.CS.YALE.EDU> Date: 3 Jan 90 14:22:03 GMT Sender: daemon@ucbvax.BERKELEY.EDU Reply-To: Richard Beigel Lines: 18 I am looking for theorems along the following lines: (a) If p(x) is a dth degree polynomial and |p(x)| < 1 for 1 <= x <= m where m is much larger than d then all the coefficients of p are very small. (b) If p(x) is a dth degree polynomial and |p(i)| < 1 for i = 1,2,...,m where m is much larger than d then all the coefficients of p are very small. (c) If p(x) is a dth degree polynomial and |p(i)| < 1 for i = 1,2,...,m where m is much larger than d then |p(x)| < 2 for 1 <= x <= m. I have some results but I suspect that this problem has already been studied. I would appreciate any leads. Thanks. -- Richard Beigel