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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
314 Chapter 9 Sample applications
For instance:
e
Œa
1
,a
2
D Œe
a
1
, e
a
2
,
Œa
1
, a
2
2n
D
(
Œmin.a
2n
1
, a
2n
2
/,max.a
2n
1
, a
2n
2
/ for 0 Œa
1
, a
2
,
Œ0, max.a
2n
1
, a
2n
2
/ for 0 2 Œa
1
, a
2
,
sinŒ=4, =4 D
h
1
2
p
2,
1
2
p
2
i
,
cosŒ0, =2 D Œ0, 1.
For non-monotonic functions the computation of the range of values over an in-
terval Œa
1
, a
2
requires the determination of the global minimum and maximum of the
function in the interval Œa
1
, a
2
. For the usual elementary functions, however, these are
known. With this definition of elementary functions for intervals, the key properties of
interval arithmetic, the inclusion monotony (9.1.5) and the inclusion property (9.1.6)
extend
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Publisher Resources

ISBN: 9783110301731