September 2003
Intermediate to advanced
709 pages
26h 51m
English
Content preview from Digital Arithmetic
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378 r H ~ {a'~ E ~ 7: Iterative Approximation
1. Error in d[j]:
edT[j ] -- edT[j
--
1 ]2 _~_
edG [j ]
7.26
where
eds[j]
includes the error in the two's complement operation and the
roundoff error in the multiplication. As in the NR method, the final error
edr[m]
is positive as long as the generated error in the last iteration is not
negative. Also generated errors are reduced quadratically.
Error in
R[j]"
If the multiplications
R[i]d
are performed in full precision,
then the error is the same as that ofd[j] (including there the errors in
roundoff and two's complement). To that error it is necessary to add the
generated errors for all ...
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