Re: Exchange algorithm (Remez or Parks-McClellan)

On Jun 9, 1:00 pm, hru...@xxxxxxxxxxxxxxxxxxxx (Herman Rubin) wrote:
In article <58b46c48-1eea-4a2e-8206-31b4351dd...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,

aruzinsky  <aruzin...@xxxxxxxxxxxxxxxxxxxx> wrote:
On Jun 7, 12:28=A0am, bubbakittee <bubbakit...@xxxxxxx> wrote:
Hi,
I'm only interested in the polynomial case, and I only need to
handle degrees of up to 30 or so.
I suspect that you will need much more than 80 bit floating point
(87x) arithemetic for polynomial degree 30.
I can't recall the maximum polynomial degree for my 80 bit
experiments, but 20 pops into my head.

It is my opinion that to handle a Remez algorithm for
10 parameters will require triple precision.  Remember
that the matrix is very ill-conditioned.
--
This address is for information only.  I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hru...@xxxxxxxxxxxxxxx         Phone: (765)494-6054   FAX: (765)494-0558

In the book,

Cecil Hastings, Jr., "Approximations for Digital Computers,"
Princteton University Press, 1955

, minimax polynomial approximations up to 8 parameters and degree 15
are given. The parameters are 10 digit. I am fairly certain that I
duplicated those results using 80 bit precision using discrete Loo
regression with my algorithm posted above.

Also, I authored,

S. A. Ruzinsky, "A Simple Minimax Algorithm," Dr. Dobb's Journal., 93,
pp 84-101, July 1984.

If and when I find my copy, I will tell everyone the number of
parameters.

.

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