R help - Feb 2006 - collocation methods

Hi R Users,

I have been trying to google (in general and specifically r-project) to see 
if I can find listing that may point me to understand the state of the art 
in R for functional approximation. Unfortunately, I have been unable to find 
anything concrete.

I hope I am missing something, and hence this message. Are there packages 
out there that may implement collocation. Specifically I am trying to 
implement Chebychev polynomial approximations.

Much more generally, has the R-management thought of some kind of 
encycopaedia that will allow developers/users to figure out what kinds of 
different routines are implemented and packaged under different packages?

thanks,
currently,

R Neeu B.

Hi All,

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

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

thanks
Alex

>>>>> "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.