Re: why extending numbers by zeros instead of dropping precision is a good idea
- To: mathgroup at smc.vnet.net
- Subject: [mg117914] Re: why extending numbers by zeros instead of dropping precision is a good idea
- From: Noqsi <noqsiaerospace at gmail.com>
- Date: Mon, 4 Apr 2011 06:30:10 -0400 (EDT)
On Mar 31, 3:06 am, Richard Fateman <fate... at 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.