Skip to Main Content
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 9.7 Multiple precision arithmetics 347
(a) an approximation x
.0/
for the correct solution x
is computed in floating-point
arithmetic by forward substitution.
(b) an enclosure E of the error e D x
x
.0/
is computed.
This leads to an enclosure for the solution:
x
2 x
.0/
C E.
Formulas for E are obtained by use of the mean value theorem. They are evaluated
by the exact scalar product.
If the quality of the enclosure x
2 x
.0/
CE is not sufficient, the midpoint x
.1/
:D
m.E/ is used to improve the approximationx
.0/
to x
.0/
Cx
.1/
. Then step (b) is repeated
and so on.
A detailed description and executable algorithms and programs can be found in
Chapter 8 of the ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Arithmetic and Logic in Computer Systems

Arithmetic and Logic in Computer Systems

Mi Lu
Interval Analysis

Interval Analysis

Günter Mayer

Publisher Resources

ISBN: 9783110301731