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Re: Bairstow Method

  • To: mathgroup at
  • Subject: [mg71801] Re: Bairstow Method
  • From: Paul Abbott <paul at>
  • Date: Wed, 29 Nov 2006 02:56:52 -0500 (EST)
  • Organization: The University of Western Australia
  • References: <ej1qbe$e45$>

In article <ej1qbe$e45$1 at>, "ms z" <ms-z- at> 

> I posted a question on how to write an automated program to solve the 
> polynomial f(x)=(x-4)(x+2)(x-1)(x+5)(x-7) (without using NSolve or Solve) 
> earlier on.
> I suggested this program: (though not a good one)
> solution := {Plot[{(x - 4)(x + 2)(x - 1)(x + 5)(x - 7)}, {x, -10, 10}, 
> AxesLabel -> TraditionalForm /@ {x, y}]}
> I've tried to write another program using Bairstow Method. But it doesn't 
> not seem to work. Could I have some help?

Mathematica code for the Lin-Bairstow method is available at

(at the end of this page).

Since Mathematica can already compute all the roots of univariate 
polynomials, why do you need to use the Lin-Bairstow method? The 
advantage of Bairstow¹s method, which seeks quadratic factors, is that 
it avoids all complex arithmetic. However, FindRoot can find all complex 


Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    

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