[Date Index] [Thread Index] [Author Index]

Re: Re: Re: 1`2 == 1*^-10

• To: mathgroup at smc.vnet.net
• Subject: [mg71707] Re: [mg71687] Re: [mg71634] Re: 1`2 == 1*^-10
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Mon, 27 Nov 2006 04:04:24 -0500 (EST)
• References: <200611251037.FAA15661@smc.vnet.net> <200611260849.DAA14709@smc.vnet.net>

On 26 Nov 2006, at 17:49, Chris Chiasson wrote:

> On 11/25/06, Bill Rowe <readnewsciv at sbcglobal.net> wrote:
>> And it doesn't seem to me there would be any
>> difficulty in rounding results to two significant digits.
>
> Yea, but I'm lazy. I once wrote some code that would do forward error
> propagation (and associated print formatting) at machine (or whatever)
> precision if given the initial errors. It has the same problem that I
> mentioned with significance arithmetic, where all errors are treated
> as independent.
>
> --  
> http://chris.chiasson.name/
>

Since Mathematica already implements forward error propagation at  
machine precision by means of the function Interval you do not seem  
to all that lazy to me ;-)

Actually, there is a way of doing this with much less overestimation  
than Interval arithmetic produces. It is called "affine arithmetic".  
There is a Mathematica implementation in a package due to Anita  
Uscilowska, which was presented at the IMS 2005.

Andrzej Kozlowski
Tokyo, Japan

• References:
  • Re: 1`2 == 1*^-10
    • From: Bill Rowe <readnewsciv@sbcglobal.net>
  • Re: Re: 1`2 == 1*^-10
    • From: "Chris Chiasson" <chris@chiasson.name>