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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
40 Chapter 1 First concepts
sum s:
s
.l/
1
5
+
s
.l/
2
5
+

5
+
s
.l/
n
(1.4.7)
n
X
iD1
s
.l/
i
(OA)
R
n
X
iD1
s
i
(OA)
R
n
X
iD1
s
.u/
i
(1.4.7)
s
.u/
1
4
+
s
.u/
2
4
+
4
+
s
.u/
n
. (1.4.8)
Equation (1.4.8) can be used, for instance, to compute lower and upper bounds of a
scalar product
n
X
iD1
a
i
b
i
, a
i
, b
i
2 S
on the computer. In this case the bounds s
.l/
i
and s
.u/
i
for the summands s
i
:D a
i
b
i
in equation (1.4.8) are obtained by
s
.l/
i
:D a
i
5
b
i
:D
(RG)
5
.a
i
b
i
/ s
i
s
.u/
i
:D a
i
4
b
i
:D
(RG)
4.a
i
b
i
/.
We stress the fact that when computing bounds for a scalar product this way the lower
(resp. upper) bound of the sum is obtained by performing all arithmetic operations with
rounding downwards (resp. upwards) ...
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Publisher Resources

ISBN: 9783110301731