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Internet Message Format  |  1992-12-30  |  979 b 
  1. Path: 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
  2. From: dhart@bronze.ucs.indiana.edu (dave hart)
  3. Newsgroups: sci.math.num-analysis
  4. Subject: Re: Chebyshev vs. Least Squares Polynomials
  5. Message-ID: <C02wr7.50A@usenet.ucs.indiana.edu>
  6. Date: 30 Dec 92 15:37:55 GMT
  7. References: <1992Dec2.170529.24897@news2.cis.umn.edu> <BzEyyF.GE0@usenet.ucs.indiana.edu>
  8. Sender: news@usenet.ucs.indiana.edu (USENET News System)
  9. Organization: Indiana University
  10. Lines: 7
  11. Nntp-Posting-Host: bronze.ucs.indiana.edu
  12.  
  13. >    The idea of "least squares" is the same as orthogonal projection--
  14. >"the shortest distance between a point and a line..."  This is tied up
  15. >with geometry, ie a metric [inner product].  The Chebyshev polynomials
  16. >form an orthonormal basis [q.v.] for the L^2 metric;  other functions
  17. >form orthonormal bases for other metrics.
  18. >
  19.     _if_ you measure with dx/sqrt(1-x^2) [what else?]. [oops!:-]
  20.