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Re: Q about Interval arithmetic

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  • Subject: [mg10567] Re: Q about Interval arithmetic
  • From: Paul Abbott <>
  • Date: Tue, 20 Jan 1998 16:54:09 -0500
  • Organization: University of Western Australia
  • References: <69nb45$> wrote:

> Is there a known algorithm that can be used to obtain the smaller (
> preferred ) Interval?
> I am not looking for an approach that uses Numerical methods as I did
> below. I want is something that provides gaurenteed results, and works
> on high  order polynomials.

A search in the Help Browser for interval finds the following useful

The package NumericalMath`IntervalRoots` provides three interval
root-finding methods: bisection, secant, and Newton's method. A nice
feature of interval root-finding methods is that they find all roots of
the given function on a given interval. More precisely, they start with
the given interval and discard parts of it that cannot possibly contain
any roots. What you end up with are some subintervals of the given
interval that are guaranteed to contain all of the roots that are
contained in the the given interval. If the roots of the given interval
are well separated then the result consists of short subintervals, each
of which contains exactly one root. 

Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907  AUSTRALIA                   

            God IS a weakly left-handed dice player

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