[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)
p3
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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