Re: numerical factorization of very high degree polynomial

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#589

From: W.A.B.Evans
Date: Wed, 07 Oct 1992 18:34

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In article <1992Oct6.094142.9281@vax.oxford.ac.uk> nagrwb@vax.oxford.ac.uk writes:
>In article <9227919.6924@mulga.cs.mu.OZ.AU>, yzhu@nairana.ee.mu.oz.au (Yan ZHU (yhua)) writes:
>> 
>>  
>>  I am trying to solve non-linear problem by LP method.
>>  And I am looking for an algorithm for the numerical
>>  factorization of very high degree (500th-800th) polynomials 
>>  with complex coefficients.
>> 
>>  ...stuff deleted 
>
>NAG Fortran Library routine C02AFF finds all the roots of a complex
>polynomial equation, usinmg a variant of Laguerre's method. Any degree
>can be specified.
>
	Another method that springs easily to mind is to find the roots
sequentially by the Newton-Raphson method within the synthetic division
algorithm. This of course converges very fast and on finding one root you
are automatically left with the coeffs. of the "deflated" polynomial and
of course, the method is perfectly suitable to polynomials with complex
coeffs. I have used this with considerable satisfaction on "moderately
large" polynomials - but certainly NOT of order 500-800. However I see no
reason why it should not work provided the calculations could be done in
"sufficiently high" precision (I doubt that COMPLEX*8 would be adequate!).

						W. Alan B. Evans
						[ wabe@ukc.ac.uk ]

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Path: arc1-ca.pugleaf.net!sparky!uunet!mcsun!uknet!harrier.ukc.ac.uk!eagle.ukc.ac.uk!wabe
From: wabe@ukc.ac.uk (W.A.B.Evans)
Newsgroups: sci.math.num-analysis
Subject: Re: numerical factorization of very high degree polynomial
Message-ID: <1787@eagle.ukc.ac.uk>
Date: 7 Oct 92 18:34:49 GMT
References: <9227919.6924@mulga.cs.mu.OZ.AU> <1992Oct6.094142.9281@vax.oxford.ac.uk>
Reply-To: wabe@ukc.ac.uk (W.A.B.Evans)
Organization: Computing Lab, University of Kent at Canterbury, UK.
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