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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 1.3 Screens and roundings 29
To illustrate the definition and the theorems given in this chapter, let us consider a
few examples.
Examples. 1. Let Z be a bounded set of complex numbers Z :Df :D C i 2
C jjjr ^jjrg. The power set fPZ, g is a complete lattice. We consider
the set IZ of all rectangles of PZ with sides parallel to the axes. The elements of IZ
are intervals in the complex plane. Also let ¿ 2 IZ. We show that fIZ, g is an upper
screen of fPZ, g.
To see this, by Theorem 1.15 we have only to show that for every subset A IZ,
the intersection, which is the infimum in fPZ, g, is an element of IZ.IfA D ¿,we
have
inf
PZ
¿ D inf
IZ
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Publisher Resources

ISBN: 9783110301731