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3D Game Engine Design, 2nd Edition
book

3D Game Engine Design, 2nd Edition

by David Eberly
November 2006
Intermediate to advanced content levelIntermediate to advanced
1040 pages
26h 31m
English
CRC Press
Content preview from 3D Game Engine Design, 2nd Edition
16.5 Root Finding 739
there are lots of matrix norms to choose from, there are many possible bounds. One
such bound is Cauchy’s bound,
|t|≤max {|a
0
|,1+|a
1
|,...,1+|a
n1
|} = 1 + max{|a
0
|,...,|a
n1
|}
Another bound that can be obtained is the Carmichael and Mason bound,
|t|≤
6
7
7
8
1 +
n1
i=0
|a
i
|
2
If a
0
= 0, then f(0) = 0, so the roots of f are bounded away from zero. It is possible
to construct lower bounds by using g(t) = [t
n
f(1/t)]/a
0
. The roots of g(t) are the
reciprocal roots of f(t). Cauchy’s bound applied to g(t), then taking reciprocals, is
|t|≥
|a
0
|
1 + max{1, |a
1
|,...,|a
n1
|}
The Carmichael and Mason bound is
|t|≥
|a
0
|
1 +
n1
i=0
|a
i
|
2
These bounds are
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Publisher Resources

ISBN: 9781482267303