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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 4.6 Interval matrices and interval vectors on a screen 123
Theorem 4.25. Let fV , R, g be a completely and weakly ordered vectoid with the
neutral elements o and e if a multiplication exists, and let fS, g be a symmetric
screen of fV , R, g. Further, let fIT, }
C
, }
g be a monotone upper screen ringoid
of fIR,
+
,
g with respect to . Consider the two semimorphisms : PV ! IV
and } :
IV ! I S .ThenfIS, IT, , g is a weakly ordered vectoid with respect to
. It is multiplicative if fV , R, g is. The neutral elements are Œo, o and Œe, e. With re-
spect to , fIS, IT, , g is an inclusion-isotonally ordered monotone upper screen
vectoid of
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Publisher Resources

ISBN: 9783110301731