Re: "Sloppy Union"? (Union of a list with *nearly* equ
- To: mathgroup at smc.vnet.net
- Subject: [mg42144] Re: "Sloppy Union"? (Union of a list with *nearly* equ
- From: AES/newspost <siegman at stanford.edu>
- Date: Fri, 20 Jun 2003 04:57:40 -0400 (EDT)
- References: <bcrs80$hr7$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bcrs80$hr7$1 at smc.vnet.net>,
Bill Rowe <listuser at earthlink.net> wrote:
> >1) Look at the heading: To allow "sloppy comparisons" within a
> >sequence of calculations -- e.g.,"Are these two complex roots
> >(probably) the same root of my physical problem?" -- **without**
> >having to stop and think about and program some lengthy
> >precision-reducing procedure **each time you make a comparison**.
>
> The heading talks about a "sloppy union". In this case it isn't an
> intermediate computation that needs to be "rounded". It is the final
> comparison that is the answer. The only real issue with a "sloppy union"
> isn't the compare step since this can be handled easily with
> Positve@Chop[Abs[#1-#2],epsilon]&. The issue is what value to output as the
> union, mean, median, min max? All of these will be the same within epsilon.
> So except for the specifics of the coding it shouldn't matter much.
Thanks, I'm beginning to understand the issues better.
Still don't grasp, however, what SetPrecision with *reduced* precision
really does, or for what purpose it might be used? For example,
SetPrecision[Pi,3] --> 3.14
Cos[y] --> -1.0
1 + y -> 4.14159
Is it nothing more that a "print wrapper" for y, and nothing else?