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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 4.2 Interval arithmetic over a linearly ordered set 97
If a multiplication exists in V , we also obtain for all A D Œa
1
, a
2
:
(F) A Œo, o ^ B Œo, o ) A
B D Œa
1
b
1
, a
2
b
2
,
(G) A Œo, o ^ B Œo, o ) A
B D Œa
2
b
2
, a
1
b
1
,
(H) A Œo, o ^ B Œo, o ) A
B D Œa
2
b
1
, a
1
b
2
,
(I) A Œo, o ^ B Œo, o ) A
B D Œa
1
b
2
, a
2
b
1
,
Proof. (a) Theorem 3.11 implies that fIV , IR, , g is a monotone upper screen vec-
toid of fP V , PRg, which is multiplicative if fV , R, g is. The inclusion-isotony is a
simple consequence of (OV5) in PV , of the monotonicity of the rounding
: PV !
IV , and of (RG). The proofs of the properties (OV1, 2, 3, 4) and (A)–( ...
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Publisher Resources

ISBN: 9783110301731