Re: Bairstow Method

*To*: mathgroup at smc.vnet.net*Subject*: [mg71801] Re: Bairstow Method*From*: Paul Abbott <paul at physics.uwa.edu.au>*Date*: Wed, 29 Nov 2006 02:56:52 -0500 (EST)*Organization*: The University of Western Australia*References*: <ej1qbe$e45$1@smc.vnet.net>

In article <ej1qbe$e45$1 at smc.vnet.net>, "ms z" <ms-z- at hotmail.com> wrote: > 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 http://math.fullerton.edu/mathews/n2003/BairstowMethodMod.html (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 roots. Cheers, Paul _______________________________________________________________________ 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) AUSTRALIA http://physics.uwa.edu.au/~paul