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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 9.7 Multiple precision arithmetics 357
If we compute an interval enclosure X
1
of e
1
,wehaveanenclosureofx
by a long
interval: x
2 x
1
C X
1
. This method can now be iterated. With a new approximate
solution x
2
:D m.x
1
CX
1
/,wherem denotes the midpoint of the interval x
1
CX
1
,a
second error e
2
can be computed by
A e
2
D b Ax
2
.
An enclosure X
2
of e
2
leads to a new enclosure of x
:
x
2 x
2
C X
2
.
Essential for success of this method is the fact that the defect b A x
i
of the
approximate solution x
i
can be computed to full accuracy by the exact scalar product.
This method of iterated defect correction can also be applied to compute with very
high accuracy enclosur ...
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Publisher Resources

ISBN: 9783110301731