Article View: sci.math.num-analysis
Article #1193Re: Sure Polynomial Roots
From: Peter Pan
Date: Fri, 06 Aug 2004 00:10
Date: Fri, 06 Aug 2004 00:10
37 lines
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2491 bytes
brianscsmith@yahoo.com (Brian Smith) wrote
>
> I see that you are no longer claiming to have solved the general
> polynomial equation, now its just a numeric formula. Why should I
> even consider this method for approximating roots when Newton's
> iteration only needs the first derivative and only a few iterations
> are needed to get the three place precesion that your method provides
> in the example. I see no need to calculate dozens of terms when it is
> so much simpler to let Newton's iteration run for more cycles.
AND ...
Jon's method calculates the solution of x - 1 = 0 as 0.7 ...
(ridiculous)
AND ...
the examples he gives on his website are NOT correctly calculated
AND
where is the notorious 'high degree of accuracy and precision'
as I said before: PLAIN BULLSHIT !!!
Hint: Use Newton's method, refined by Householder:
(1/p)k
x_(n+1)=x_n + (k+1)*------------(x_n)
(1/p)(k+1)
[the 'k' and 'k+1' at the (1/p)'s intends to mean k-th resp. (k+1)-th
derivative]
to obtain an approximation of real roots at an order of k+2 (iff you
have an appropriate starting value)
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X-Google-Thread: 107079,dfd14b9e0d1043ac X-Google-Thread: 109d8a,dfd14b9e0d1043ac X-Google-Thread: f72df,dfd14b9e0d1043ac X-Google-Thread: 103471,dfd14b9e0d1043ac X-Google-Thread: 1139f8,dfd14b9e0d1043ac X-Google-Thread: 10d67e,dfd14b9e0d1043ac X-Google-Thread: 1130d6,dfd14b9e0d1043ac X-Google-Thread: f6df2,dfd14b9e0d1043ac X-Google-Attributes: gid107079,gid109d8a,gidf72df,gid103471,gid1139f8,gid10d67e,gid1130d6,gidf6df2,public X-Google-Language: ENGLISH,ASCII-7-bit Path: arc1-ca.pugleaf.net!g2news1.google.com!postnews2.google.com!not-for-mail From: RMoebs1@compuserve.de (Peter Pan) Newsgroups: sci.math.num-analysis,sci.math,japan.sci.math,han.sci.math,fr.sci.maths,aus.mathematics,alt.math.recreational,bln.sci.mathematik Subject: Re: Sure Polynomial Roots Date: 5 Aug 2004 17:10:56 -0700 Organization: http://groups.google.com Lines: 37 Message-ID: <3cc72195.0408051610.58e54b2c@posting.google.com> References: <4111D4FB.8050608@peoplepc.com> <12f59340.0408050442.77cdea79@posting.google.com> NNTP-Posting-Host: 84.129.104.53 Content-Type: text/plain; charset=ISO-8859-1 Content-Transfer-Encoding: 8bit X-Trace: posting.google.com 1091751056 12980 127.0.0.1 (6 Aug 2004 00:10:56 GMT) X-Complaints-To: groups-abuse@google.com NNTP-Posting-Date: Fri, 6 Aug 2004 00:10:56 +0000 (UTC)