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From: ashby@uiucdcsp.CS.UIUC.EDU
Newsgroups: net.math
Subject: Re: cubic roots
Message-ID: <9600019@uiucdcsp>
Date: Tue, 15-Oct-85 13:07:00 EDT
Article-I.D.: uiucdcsp.9600019
Posted: Tue Oct 15 13:07:00 1985
Date-Received: Thu, 17-Oct-85 23:34:13 EDT
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Nf-From: uiucdcsp.CS.UIUC.EDU!ashby    Oct 15 12:07:00 1985


There is an "easy" closed formula for the roots of an arbitrary
cubic (and quartic).  You should be able to find it in any book
of mathematical formulae (eg, CRC).  However, if you need to 
compute these roots, then the formulae are not very good.

The following "algorithm" is a numerically stable way of computing
the roots of any nth degree polynomial (n not too big):

1)  Set up the poly's companion matrix.  (This is defined in almost
    any linear algebra book.)

2)  Now compute the eigenvalues of the matrix.  To do this the
    package EISPACK is recommended.  (If you don't have this 
    pkg, you should get it; it is in the public domain.)

3)  These egvals are the desired roots of the poly.