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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
118 Chapter 4 Interval arithmetic
4.6 Interval matrices and interval vectors on a screen
We begin with the following characterization of IM
n
S.
Theorem 4.23. Let fR, C, , gbe the completely and linearly ordered ringoid of real
numbers and fS, ga symmetric screen of R. Consider the completely ordered ringoid
of matrices fM
n
R, C, , gwith the neutral elements O and E and the semimorphisms
: PM
n
R ! IM
n
R and } : IM
n
R ! IM
n
S.ThenfIM
n
S, }
C
, }
, , g is a
completely ordered ringoid with respect to . The neutral elements are ŒO, O and
ŒE, E. With respect to , IM
n
S is an inclusion-isotonally ordered monotone upper
screen ringoid of IM
n
R.
Proof. Theorem ...
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Publisher Resources

ISBN: 9783110301731