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MathGroup Archive 2007

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Re: Approximate/asymptotic factorization

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73573] Re: Approximate/asymptotic factorization
  • From: Roger Bagula <rlbagula at sbcglobal.net>
  • Date: Thu, 22 Feb 2007 04:31:30 -0500 (EST)
  • References: <ergpj1$h7f$1@smc.vnet.net>

Paul Abbott wrote:

>Consider the monomial H[4,4]
>
>  256*(23625 + 126000*z^4 - 7200*z^8 + 3840*z^12 + 256*z^16)
>
>
>
>Then consider the monomial Q[4,4]
>
>  1528899609315374375625 + 6795109374734997225000*z^4 -  
>  560866170613047390000*z^8 + 153399294526645440000*z^12 +  
>  2734590598399296000*z^16 - 167891551278796800*z^20 +  
>  2948686820352000*z^24 - 40649991782400*z^28 +  277762867200*z^32 - 
>  920125440*z^36 + 1048576*z^40
>
>
>
>  
>
It is a scale problem in the roots:
-1.5394683843101908/(-1.4575368807601277)
1.0562123021596095

q[x_] = ExpandAll[256*(23625 + 126000*z^4 -
        7200*z^8 + 3840*z^12 + 256*z^16) /. z -> (x/1.0562123021596095)]

(6048000 + 2.591824698102241`*^7 x^4 - 1.1900430955379773`*^6 x^8 +
509983.9759955976` x^12 + 27318.722400416882` x^16)

c = Table[{Re[x], Im[x]} /. NSolve[q[x] == 0, x][[n]], {n, 1, 16}]

This sub-polynomial gives very close to the same roots for the square 
lattice of roots at the center of z^40 polynomial.


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