piecewise polynomial function convolution

This turns out not to be such a good idea.  My thought was to be able to compute convolutions of functions outputted by 
the cspline() function in interpol.mac.  I have implemented the algorithm in Maxima but for most cases it takes too 
long.  The problem is that the number of pieces in the piecewise function answer can get very, very large and each time 
you do a convolution you are making the answer larger and larger (exponentially I think).  I think it is impractical to 
do it this way.  The good news is the answer does get closer and closer to looking like a Gaussian but it is not a 
Gaussian.  Exact solutions for more complicated cases are possible if you have a lot a parallel CPU's working on the 
answer but this cannot be done in Maxima yet.

Maybe there is an approximation technique for getting a good answer numerically.  I don't know of any and I hesitate to 
take on the task of coming up with one as I am rather mathematically naive.

Anyway it was worth a try.

Rich




From: Stavros Macrakis
Sent: Monday, May 03, 2010 9:43 PM
To: Richard Hennessy
Cc: Maxima List
Subject: Re: [Maxima] piecewise polynomial function convolution


IANAL, but... you can't copyright an algorithm, only specific code to implement it. US patents expire after 17-20 years, 
so any patents on something published in 1973 would have expired some time ago.

                -s




On Mon, May 3, 2010 at 21:22, Richard Hennessy <rich.hennessy at verizon.net> wrote:

  Hi list,

  I found this link during a search for something else unrelated to the subject of the article.  When I came across it I 
got curious and read it. I may want to use this method with a new pwpolyint(L,x) function. I was wondering if there is a 
copyright on the method of integration they discovered and is it free to use the algorithm.

  http://degiorgi.math.hr/~singer/aaa_sem/ZZ_NOT_NOW /970-975.pdf

  Any ideas?  Is it worth the effort?

  Rich




  _______________________________________________
  Maxima mailing list
  Maxima at math.utexas.edu
  http://www.math.utexas.edu/mailman/listinfo/maxima