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

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

> On 11/25/06, Bill Rowe <readnewsciv at> 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.
> --  

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

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