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Re: RE: Solving the Cubic

  • To: mathgroup at
  • Subject: [mg71916] Re: [mg71883] RE: [mg71859] Solving the Cubic
  • From: Murray Eisenberg <murray at>
  • Date: Sun, 3 Dec 2006 06:26:52 -0500 (EST)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <>
  • Reply-to: murray at

So far as I know, Vieta's method is not intended for numeric 
approximation.  Rather, it is intended to give EXACT solutions in terms 
of algebraic operations.  It's the "cubic formula", analogous to the 
quadratic formula.  (One would not typically use the quadratic formula 
to give good numeric solutions of quadratics, after all.)

Mark Harder wrote:
> Dimitris,
> 	Symbolic solutions can be very error- and precision- sensitive (See
> Press, et al, "Numerical Recipes.." for a trick that stabilizes quadratic
> solutions.)  Do you know if Vieta's method designed to avoid numeric
> instabilities?
> Mark Harder
> -----Original Message-----
> From: dimitris [mailto:dimmechan at] 
> Sent: Friday, December 01, 2006 3:22 AM
> To: mathgroup at
> Subject: [mg71883] [mg71859] Solving the Cubic
> The following cell follows the Vieta's method for solving the cubic
> equation complete with all the necessary steps and text explanations.
> I really appreciate any kind of comments.
> (code omitted ).

Murray Eisenberg                     murray at
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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