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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 9.5 Verified solution of systems of linear equations 333
Again, we illustrate this process by a simple example. The starting interval is de-
noted by X D Œx
1
, x
2
and the result of the Newton operator by N D Œn
1
, n
2
.See
Figure 9.8.
xx
2
x
1
n
2
n
1
x
f.x/
f.x/
XN.X/N.X/
D Œx
1
, n
2
[ Œn
1
, x
2
D N.X/ \ XX
1
Figure 9.8. Geometric interpretation of the extended interval Newton method.
Now F
0
.X/ is again a superset of all slopes of tangents of f.x/in the interval X D
Œx
1
, x
2
. But now 0 2 F
0
.X/.ThesetN.X/ again is the set of zeros of straight lines
through .x, f.x//with slopes within F
0
.X/.LetF
0
.X/ D Œs
1
, s
2
.Since02 F
0
.X/
we have s
1
0ands
2
0. The straight
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Publisher Resources

ISBN: 9783110301731