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Re: why extending numbers by zeros instead of dropping precision is a good idea

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  Re: why extending numbers by zeros instead of dropping precision is a good idea Noqsi <noqsiaerospace@gmail.com> - 2011-04-04 10:30 +0000

#1454 — Re: why extending numbers by zeros instead of dropping precision is a good idea

On Mar 31, 3:06 am, Richard Fateman <fate...@eecs.berkeley.edu> wrote:
> It is occasionally stated that subtracting nearly equal quantities from
> each other is a bad idea and somehow unstable or results in noise. (JT
> Sardus said it on 3/29/2011, for example.)
>
>   This is not always true; in fact it may be true hardly ever.

Hardly ever? What a silly assertion. This has been a major concern
since the dawn of automatic numerical analysis.

>
>   It is, for example, the essence of Newton iteration.

Convergence on a fixed point is a special case. Negative feedback
attenuates error (your homework today is to study how the delta-sigma
method can extract 24 bit accuracy from a 1 bit digitizer). But many
numerical methods lack negative feedback.

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