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Article #935Re: Chebyshev vs. Least Squares Polynomials
From: dave hart
Date: Wed, 30 Dec 1992 15:37
Date: Wed, 30 Dec 1992 15:37
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> The idea of "least squares" is the same as orthogonal projection-- >"the shortest distance between a point and a line..." This is tied up >with geometry, ie a metric [inner product]. The Chebyshev polynomials >form an orthonormal basis [q.v.] for the L^2 metric; other functions >form orthonormal bases for other metrics. > _if_ you measure with dx/sqrt(1-x^2) [what else?]. [oops!:-]
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Path: arc1-ca.pugleaf.net!sparky!uunet!munnari.oz.au!spool.mu.edu!agate!stanford.edu!rutgers!news.cs.indiana.edu!usenet.ucs.indiana.edu!bronze.ucs.indiana.edu!dhart From: dhart@bronze.ucs.indiana.edu (dave hart) Newsgroups: sci.math.num-analysis Subject: Re: Chebyshev vs. Least Squares Polynomials Message-ID: <C02wr7.50A@usenet.ucs.indiana.edu> Date: 30 Dec 92 15:37:55 GMT References: <1992Dec2.170529.24897@news2.cis.umn.edu> <BzEyyF.GE0@usenet.ucs.indiana.edu> Sender: news@usenet.ucs.indiana.edu (USENET News System) Organization: Indiana University Lines: 7 Nntp-Posting-Host: bronze.ucs.indiana.edu