On Wed, 23 Nov 2005 20:43:09 +0000 (UTC), molnar@rtp.ericsson.se (Karl
Molnar) wrote:

>In article <1132777446.921670.252430@o13g2000cwo.googlegroups.com>,
> "Randy Yates" <yates@ieee.org> writes:
>>Karl,
>>
>>I'm sorry I missed him. Was it a good meeting?
>>
>>--Randy
>>
>
>Randy,
>
>It was interesting - he spoke about the history and application of the cepstrum.
>As an added bonus, we also met Jim Kaiser.
>
>Karl

Hi,

   meeting Schafer and Kaiser must have been like 
a baseball fan meeting Ted Williams & Mickey Mantle.

Neat.

[-Rick-]

I should've gone. Cool stuff, venerable men.

--Randy

Emile wrote:

(snip)

> I have had a course on computerarithmetics, there we used iterative 
> methods to gradually come closer to the root(s) up to some arbitrary 
> small error (by using the output of one iteration as input for the next, 
> and stop when 2 successive iterations differ very little (other stopping 
> conditions may be better but its usable), the fastest algorithm we've 
> seen was the Newton-Raphson method (maybe not the fastest that exists). 

For a simple root, that is fine.  For a multiple root the derivative 
goes to zero at the root, which is inconvenient for Newton's method.

-- glen

Thank you to you all :o)

In article <1132777446.921670.252430@o13g2000cwo.googlegroups.com>,
 "Randy Yates" <yates@ieee.org> writes:
>Karl,
>
>I'm sorry I missed him. Was it a good meeting?
>
>--Randy
>

Randy,

It was interesting - he spoke about the history and application of the cepstrum.
As an added bonus, we also met Jim Kaiser.

Karl

John wrote:
>> Why do you want them?  If it is to check for stability, that is
> 
> It is not to check for stability....It is because I am more interested in 
> finding the roots than the LPC-coefficients. If I have the roots I can 
> quickly calculate the LPC-coefficients if I want to....so I am looking for a 
> _fast_ way of determining the roots of a 10th order polynomial...I see that 
> matlab solves it as an eigenvalue-problem....Is this the fastest way?

No.  See:

   http://www.dsp.rice.edu/software/fvhdp.shtml


Bob
-- 

"Things should be described as simply as possible, but no simpler."

                                              A. Einstein

Karl,

I'm sorry I missed him. Was it a good meeting?

--Randy

In article <43847dd4$0$67257$157c6196@dreader2.cybercity.dk>,

 "John" <johnjohn@sucker.com> writes:
>> Why do you want them?  If it is to check for stability, that is
>
>It is not to check for stability....It is because I am more interested in 
>finding the roots than the LPC-coefficients. If I have the roots I can 
>quickly calculate the LPC-coefficients if I want to....so I am looking for a 
>_fast_ way of determining the roots of a 10th order polynomial...I see that 
>matlab solves it as an eigenvalue-problem....Is this the fastest way?

Just went to a talk by Ron Shafer last night, and he talked about the problem
of finding roots of very high degree polynomials (up to order 1 million) using
a technique published in "Factoring Very High Degree Polynomials," IEEE Signal
Processing Magazine, November 2003.  You can get more info at
http://www-dsp.rice.edu/software/fvhdp.shtml

Regards,
Karl Molnar

Yes.


-----
< Do you *really* need them? Having spent a

John wrote:
> > Why do you want them?  If it is to check for stability, that is
>
> It is not to check for stability....It is because I am more interested in
> finding the roots than the LPC-coefficients. If I have the roots I can
> quickly calculate the LPC-coefficients if I want to....so I am looking for a
> _fast_ way of determining the roots of a 10th order polynomial...I see that
> matlab solves it as an eigenvalue-problem....Is this the fastest way?

I have solved roots in polynomials by using Laguerre's method. It works

reasonably well for 5th order polynomials, but requires a fair amount
of
fiddling to obtain a stable, robust method.

Before embarking on implementing such a routine, you should consider
why you want these roots. Do you *really* need them? Having spent a
bit of time with these things recently, I find it hard to justify the
effort
without a very compelling reason. For the record: The reason why I did
these things was that I wanted to represent IIR bandpass and bandstop
filters as a sequence of 2nd order sections. I am still debugging the
routines, three months after I started to implement them.

Rune