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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
Chapter 1
First concepts
In this chapter we give an axiomatic characterization of the essential prop-
erties of the sets and subsets shown in Figure 1. We then define the notion
of rounding from a set M onto a subset N and study the key properties of
certain special roundings and their interactions with simple arithmetic op-
erations. To accomplish this, we employ several lattice theoretic concepts
that are developed at the beginning of this chapter.
1.1 Ordered sets
The spaces listed in column two of Figure 1 are part of analysis. As such they carry
three k inds of mathematical structures: an algebraic structure, a topological or metric
structure, and an order structure. These are coupled by certain compatibility properties,
for instance: a b ) a
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Publisher Resources

ISBN: 9783110301731