Re: "Sloppy Union"? (Union of a list with *nearly* equ
- To: mathgroup at smc.vnet.net
- Subject: [mg42119] Re: "Sloppy Union"? (Union of a list with *nearly* equ
- From: Bill Rowe <listuser at earthlink.net>
- Date: Thu, 19 Jun 2003 04:00:14 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
On 6/18/03 at 2:11 AM, siegman at stanford.edu (AES/newspost) wrote: >In article <bcmq9f$ssn$1 at smc.vnet.net>, Bill Rowe ><listuser at earthlink.net> wrote: > >>No, this won't suffice. N isn't intended to control the output >>display. More to the point why would you want to reduce the precision >>of intermediate computations? >Answers: >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. >2) More generally: When you're doing a series of calculations based >on imprecise inputs (e.g., from imprecise physical measurements) and >you neither need nor even want more precision than that. Mathematica won't give you more precision in the final answer than the precision in the inputs. Mathematica may display more digits in the answer than the precision. And there are specific commands for controlling the display of numbers as needed. And this still doesn't address my question. If you reduce precision of intermediate steps you reduce precision of the answer. You have the potential of having less precision in the final answer than you did in the inputs by doing this. I see no point in reducing precision before the final answer is obtained.