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From: bob@dolores.Stanford.EDU (Bob Lodenkamper)
Newsgroups: comp.sys.handhelds
Subject: Re: Finding roots of Tertiary and above equations?
Message-ID: <BOB.91May17165906@dolores.Stanford.EDU>
Date: 17 May 91 23:59:06 GMT
References: <22117@shlump.nac.dec.com> <283322a6:
	2812.1comp.sys.handhelds;1@hpcvbbs.UUCP>
	<1991May17.230122.21758@zoo.toronto.edu>
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Organization: Computer Systems Laboratory, Stanford University
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In-Reply-To: henry@zoo.toronto.edu's message of Fri, 17 May 1991 23:01:22 GMT

In article <1991May17.230122.21758@zoo.toronto.edu> henry@zoo.toronto.edu (Henry Spencer) writes:
   There are formulas for cubics (3rd power) (slightly long) and quadrics
   (4th power) (seriously long), but provably none for quintics and up.

   Something like HP's numerical solver is often rather more useful in any
   case.  Even with quadratics it's easy to find cases where the subtraction
   operation in the formula nearly destroys the precision of the result,
   while numerical techniques don't have that problem.

I agree that numerical solutions are often more useful for 3rd and 4th
degree equations, but I don't agree with the statement that numerical
methods of solution don't have numerical problems.  Certainly one
can avoid a catastrophic cancellation, but closely spaced or multiple
roots are always difficult to compute accurately.  

- Bob