[R] collocation methods

Martin Maechler maechler at stat.math.ethz.ch
Tue Mar 7 09:11:36 CET 2006

>>>>> "Alex" == Alexander Nervedi <alexnerdy at hotmail.com>
>>>>>     on Mon, 06 Mar 2006 17:31:40 +0000 writes:

    Alex> Hi All, I have found the function poly(), that
    Alex> computes orthogonal polynomials. I was wondering if
    Alex> there are users of this function on the list. What
    Alex> kind of an orthognal polynomial is this fititng ? Is
    Alex> it, for example, least square, galerkin, or
    Alex> collocation ?

poly() computes an orthogonal *basis*, orthogonal with respect to
the simple n-dimensional scalar product  <u,v> :=  sum_{i=1}^n  u_i * v_i

and where the k-th basis vector is a k-th order polynomial in
the arguments of poly. 

This should clear from  ?poly  -- did you read that?

Maybe the following helps:

  x <- c(0:3,5,7,11,13,17,19)
  p3 <- poly(x, degree=3)
  matplot(x, p3, type = "o")

One important use of poly() is in a formula which is used in
lm().  In that case, of course least squares polynomials are fit.

Martin Maechler, 
ETH Zurich

    Alex> It references Chambers and Hastie, and Kennedy and
    Alex> Gentle, but I dont have access to either.

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