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Computer Arithmetic and Validity
book

Computer Arithmetic and Validity

by Ulrich Kulisch
April 2013
Intermediate to advanced content levelIntermediate to advanced
456 pages
16h 7m
English
De Gruyter
Content preview from Computer Arithmetic and Validity
Section 1 .4 Arithmetic ope rations a n d roundings 35
Finally we show by simple examples that in general Lemma 1.29 and Theorem 1.30
are not valid in the case of a complete but not linearly ordered lattice. Let fM , g be
the complete lattice that appears in Figure 1.11 (a).
i.M/
(a) (b)
o.M/
e
c
a
b
d
f
c
ab
d
z
Figure 1.11. Roundings in nonlinearly ordered sets.
The subset fS, g consisting of the solid points in Figure 1.11 (a) obviously is a
screen of fM , g. We define a mapping
: M ! S by the following properties:
1. All screenpoints are fixed points of the mapping.
2.
a D b, c D d , e D f . See Figure 1.11 (a).
Then
is a monotone rounding. However, neither Lemma ...
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Publisher Resources

ISBN: 9783110301731