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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 5.2 Floating-point numbers and roundings 163
2.
1
3
1
3
D
1
9
or 0.33333 ::: 0.33333 :::D 0.11111 :::
n
n
s
n
1 0.09 0.1
2 0.1089 0.11
3 0.110889 0.111
4 0.11108889 0.1111
.
.
.
.
.
.
.
.
.
Note that this example also shows that using double precision arithmetic does not
guarantee single precision accuracy. Nevertheless, the real number s is well defined
as the limit of the sequence f
n
g. The irrational numbers can be defined as Cauchy
sequences of rational numbers. Two sequences are equivalent if they have the same
limit. In this sense f
n
g and fs
n
g both belong to the equivalence class that defines s.
The first part o f this book is intended to provide an abstr ...
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Publisher Resources

ISBN: 9783110301731