From bug-request at octave dot org Tue Jul 27 18:35:35 2004
Subject: Re: root (x^{1/n}) inconsistency or problem ?
From: Paul Kienzle <pkienzle at users dot sourceforge dot net>
To: "Pascal A. Dupuis" <Pascal dot Dupuis at esat dot kuleuven dot ac dot be>
Cc: bug at octave dot org
Date: Tue, 27 Jul 2004 19:34:42 -0400

On Jul 27, 2004, at 11:23 AM, Pascal A. Dupuis wrote:

> I work a lot on System Identification problems, and I often have to
> find the roots of some real polynomial, which must be design occur as
> complex conjugate pairs, if any. So, performing operations on a
> complex vector x where imag(sum(x)) is constrained to be 0 should
> result in a vector with the same constraint. Thus, for exponentiating
> with m = 1/n, n integer > 1:
>
> positive real value: OK
> complex conjugate pair: return the principal value,
> 	i.e. abs(c)^m*exp(+/-arg*m*j)
> negative real value, n even: result has to be complex
> 		     n odd:  I would prefer - (abs(x))^1/n, which is
> 		     real and such that result ^n = x
>
> I agree that, with this approach, this opens another problem,
> i.e. detecting that m is the reciprocal of some integer.

Have you looked at Algorithm 835: MultRoot---a Matlab
package for computing polynomial roots and multiplicities in
TOMS?  It claims " MultRoot is a collection of Matlab modules
for accurate computation of polynomial roots, especially roots
with non-trivial multiplicities."

Let us know how it works.

- Paul



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