*To*: mathgroup@smc.vnet.net*Subject*: [mg10567] Re: Q about Interval arithmetic*From*: Paul Abbott <paul@physics.uwa.edu.au>*Date*: Tue, 20 Jan 1998 16:54:09 -0500*Organization*: University of Western Australia*References*: <69nb45$886@smc.vnet.net>

Ersek_Ted%PAX1A@mr.nawcad.navy.mil 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 information: 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. Cheers, Paul ____________________________________________________________________ Paul Abbott Phone: +61-8-9380-2734 Department of Physics Fax: +61-8-9380-1014 The University of Western Australia Nedlands WA 6907 mailto:paul@physics.uwa.edu.au AUSTRALIA http://www.pd.uwa.edu.au/~paul God IS a weakly left-handed dice player ____________________________________________________________________