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Re: Re: Change in NSolve algorithm

• To: mathgroup at smc.vnet.net
• Subject: [mg98569] Re: [mg98545] Re: Change in NSolve algorithm
• From: Mark McClure <mcmcclur at unca.edu>
• Date: Mon, 13 Apr 2009 03:32:37 -0400 (EDT)
• References: <grpif7$lnr$1@smc.vnet.net> <200904120747.DAA27216@smc.vnet.net>

On Sun, Apr 12, 2009 at 3:47 AM, ADL <alberto.dilullo at tiscali.it> wrote:

> What surprised me about Wilkinson's polynomial example, which should
> return Range[20], is the following.
>
> Mathematica Help says that: "NSolve[eqns,vars,n] gives results to n-
> digit precision". Consequently, omitting n should imply machine
> precision.


And, in fact, both of your examples that use the optional third argument
are correct to the requested number of digits.  Note that the results are
not machine precision numbers, even when you requested the results
to $MachinePrecision.  Rather, they are arbitrary precision numbers
that happen to be correct to $MachinePrecision.  Mathematica can
track the precision of such numbers and make adjustments along the
way to generate a result of any desired precision.  Intermediate results
may require much more precision, however.  Computations done
using machine precision, however, are done using your machine's
standard floating point arithmetic which offers no such error tracking.

Bottom line: Not a bug but, rather, standard behavior in numerical
analysis.

Mark

• References:
  • Re: Change in NSolve algorithm
    • From: ADL <alberto.dilullo@tiscali.it>