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Fig. 14.5
Wavelet compression of the Lévy measure for level
L
=
7in
d
=
1
,
2
,
3
If
p>
2
dp
−
(d
+
1
)α and α
≤
2
/d
,
the number of non-zero entries for the com-
pressed matrix
A
J
(
2
L
L
2
(d
−
1
)
)
.
is
O
We give an example for the matrix compression for various dimensions.
1,
a
=
Example 14.6.2
Let
a
=
1,
p
=
2,
p
=
4,
α
=
0
.
5 and
L
=
7. The corre-
sponding compression scheme is plotted in Fig.
14.5
for
d
1
,
2
,
3. Zero entries
due to the first compression are left white, zero entries due to the second compres-
sion are colored red and non-zero entries are blue regardless of their size. For
d
=
=
1,
there are 14 % of non-zero entries, for
d
=
2 one has 28 % and for
d
=
3, we have
43 %.
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