From: Pawel <prulikowski@REMOVEgmail.com>
Path: news.mathworks.com!newsfeed-00.mathworks.com!webcrossing
Newsgroups: comp.soft-sys.matlab
Subject: Re: Polynomial roots
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Date: Thu, 7 Sep 2006 06:01:25 -0400
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pisz_na.mirek wrote:
>
>
> Pawel <prulikowski@removegmail.com> wrote:
>> Hello,
>>
>> I am trying to find roots of a polynomial of the form:
>>
>> (1-d*x^(-1))*(1-conj(d)*x)-b^2=0
>>
>> d is complex number,
>> b is real number,
>>
>> The main problem is how to make Matlab interpret properly
orders
> of
>> the polynomial - some of them are negative some positive.
>
> Your equation is equivalent to:
>
> 2 2 2
> d x + (- d + b - 1) x + d
> - ---------------------------- = 0
> x
>
> then your answer is: roots([ d, -d^2+b^2-1, d ])
> or analitically solved:
>
> 4 2 2 4 2 2 2
> SQRT(d + (- 2 b - 2) d + b - 2 b + 1) - d + b - 1
> x = - --------------------------------------------------------
> 2 d
>
> 4 2 2 4 2 2 2
> SQRT(d + (- 2 b - 2) d + b - 2 b + 1) + d - b + 1
> x = --------------------------------------------------------
> 2 d
>
>

Hello Mirek,

Thanks a lot for all your suggestions - the problem is slightly more
complicated as the actual, proper equation looks like this:

_N
||[(1-dk*x^(-1))*(1-conj(dk)*x)]-b^2=0
k=1

How would you handle this problem ?

Regards

Pawel