Операторы в вейвлетном базисе
bet(i+L)=HI_D(k-L)*LO_D(k1-L)*R(2*i+k-k1+L)+bet(i+L);
gam(i+L)=LO_D(k-L)*HI_D(k1-L)*R(2*i+k-k1+L)+gam(i+L);
end;
end;
end;
end;
ПРИЛОЖЕНИЕ
3
Вейвлет
Добеши с M=2.
a1=1.1250
a3=-0.1250
r1=-0.6667
r2=0.0833
Вейвлет
Добеши
с M=3.
a1=1.1719
a3=-0.1953
a5=0.0234
r1=-0.7452
r2=0.1452
r3=-0.0146
r4=-0.0003
Вейвлет
Добеши
с
M=4.
a1=1.19628906249870
a3=-0.23925781249914
a5=0.04785156250041
a7=-0.00488281249997
r1=-0.79300950497055
r2=0.19199897079726
r3=-0.03358020705113
r4=
0.00222404967066 r5=0.00017220619000
r6=-0.00000084085054
Вейвлет
Добеши с
M=5.
a1=1.21124267578280
a3=-0.26916503906311
a5=0.06921386718738
a7=-0.01235961914130
a9=0.00106811523422
r1=-0.82590601185686
r2=0.22882018706986
r3=-0.05335257193327
r4=0.00746139636621
r5=-0.00023923581985
r6=-0.00005404730164
r7=-0.00000025241171
r8=-0.00000000026960
- Вейвлет
Добеши
с M=6.
a1=1.22133636474683
a3=-0.29079437255810
a5=0.08723831176674
a7=-0.02077102661228
a9=0.00323104858448
a11=-0.00024032592766
r1=-0.85013666156022
r2=0.25855294414318
r3=-0.07244058999853
r4=0.01454551104340
r5=-0.00158856154379
r6=0.00000429689148
r7=0.00001202657519
r8=0.00000042069120
r9=-0.00000000289967
r10=0.00000000000070
Вейвлет
Койфмана с
M=2.
a1=1.20035616471068
a3=-0.24753371156550
a5=0.05401594511476
a7=-0.00724698442340
a9=0.00043220193586
a11=-0.00002361577240
r1=-0.80177838961957
r2=0.20214744976459
r3=-0.03943577686925
r4=0.00404789045961
r5=-0.00008445623632
r6=0.00000255044096
r7=0.00000088836508
r8=0.00000000237860
r9=-0.00000000002099
r10=0.00000000000000
- Симлет
с M=2.
a1=1.12499999999971
a3=-0.12499999999971
r1=-0.66666666666616
r2=0.08333333333308
- Симлет
с M=3.
a1=1.17187500000666
a3=-0.19531250000432
a5=0.02343749999766
r1=-0.74520547946903
r2=0.14520547945865
r3=-0.01461187214494
r4=-0.00034246575336
- Симлет
с M=4.
a1=1.19628906249990
a3=-0.23925781249985
a5=0.04785156249993
a7=-0.00488281249998
r1=-0.79300950497424
r2=0.19199897079876
r3=-0.03358020705098
r4=0.00222404967071
r5=0.00017220619000
r6=-0.00000084085054
ПРИЛОЖЕНИЕ
4
Вейвлет
Добеши с M=2.
|
α-3=-0.00520833333331
|
β-3
=-0.00139556871057
|
γ-3=0.01943776462271
|
|
α-2=0.04687500000004
|
β-2=0.02222890204378
|
γ-2=-0.04027109795592
|
|
α-1=0.71874999999873
|
β-1=-0.03887552924536
|
γ-1=0.00279113742108
|
|
α1=-0.71874999999873
|
β1=-0.00279113742108
|
γ1=0.03887552924536
|
|
α2=-0.04687500000004
|
β2=0.04027109795592
|
γ2=-0.02222890204378
|
|
α3=0.00520833333331
|
β3=-0.01943776462271
|
γ3=0.00139556871057
|
- Вейвлет
Добеши с M=3.
|
α-5=
-0.00000401327055
|
β-5
=0.00000042496289
|
γ-5=-0.00003790058109
|
|
α-4=0.00173507063342
|
β-4=-0.00018594182937
|
γ-4=
0.01618803080395
|
|
α-3=
-0.01438088613327
|
β-3=
0.00249383057321
|
γ-3=
-0.05023776816965
|
|
α-2=
0.09779091752885
|
β-2=-0.02225975249164
|
γ-2=0.03807446337594
|
|
α-1=0.84450449488848
|
β-1=0.05176823864378
|
γ-1=0.02782997442973
|
|
α1=
-0.84450449488848
|
β1=
-0.02782997442973
|
γ1=-0.05176823864378
|
|
α2=-0.09779091752885
|
β2=
-0.03807446337594
|
γ2=
0.02225975249164
|
|
α3=
0.01438088613327
|
β3=
0.05023776816965
|
γ3=
-0.00249383057321
|
|
α4=
-0.00173507063342
|
β4=-0.01618803080395
|
γ4=0.00018594182937
|
|
α5=0.00000401327055
|
β5=0.00003790058109
|
γ5=-0.00000042496289
|
Вейвлет
Добеши
с M=4.
|
α-7=0.00000000205286
|
β-7
=0.00000000009443
|
γ-7=-0.00000004462725
|
|
α-6=-0.00000544992677
|
β-6
=-0.00000025123058
|
γ-6=0.00011822433115
|
|
α-5=-0.00041543477135
|
β-5
=-0.00001769213018
|
γ-5=0.00969983443149
|
|
α-4=0.00432716179594
|
β-4=0.00030224225713
|
γ-4=
-0.04151919818136
|
|
α-3=-0.02134228538239
|
β-3=-0.00242879427312
|
γ-3=
0.05677199535135
|
|
α-2=0.14516544960962
|
β-2=0.01699891329704
|
γ-2=-0.00862627283270
|
|
α-1=0.93050197130889
|
β-1=-0.04758076037403
|
γ-1=-0.04917088083201
|
|
α1=-0.93050197130889
|
β1=
0.04917088083201
|
γ1=0.04758076037403
|
|
a2=-0.14516544960962
|
β2=
0.00862627283270
|
γ2=-0.01699891329704
|
|
a3=0.02134228538239
|
β3=
-0.05677199535135
|
γ3=0.00242879427312
|
|
α4=-0.00432716179594
|
β4=0.04151919818136
|
γ4=-0.00030224225713
|
|
a5=0.00041543477135
|
β5=-0.00969983443149
|
γ5=0.00001769213018
|
|
a6=0.00000544992677
|
β6=-0.00011822433115
|
γ6=0.00000025123058
|
|
α7=-0.00000000205286
|
β7=
0.00000004462725
|
γ7=-0.00000000009443
|
- Симлет
с M=2.
|
α-3=-0.00520833333331
|
β-3
=-0.00139556871057
|
γ-3=0.01943776462271
|
|
α-2=0.04687500000004
|
β-2=0.02222890204378
|
γ-2=-0.04027109795592
|
|
α-1=0.71874999999873
|
β-1=-0.03887552924536
|
γ-1=0.00279113742108
|
|
α1=-0.71874999999873
|
β1=-0.00279113742108
|
γ1=0.03887552924536
|
|
α2=-0.04687500000004
|
β2=0.04027109795592
|
γ2=-0.02222890204378
|
|
α3=0.00520833333331
|
β3=-0.01943776462271
|
γ3=0.00139556871057
|
ЛИТЕРАТУРА
Beylkin G. Wavelets
and Fast Numerical Algorithms
Beylkin G.
Wavelets, Multiresolution Analysis and Fast Numerical Algorithms
Beylkin G. In The
Representation.of Operators in Bases of Compactly Supported Wavelets
Bradley K. Alpert A
Class of Bases in L2
for the Sparse Representation of Integral Operators
Дремин
И.М., Иванов О.В.,
Нечитайло В.А.
Вейвлеты и их
использование
// Успехи физических
наук – 2001, №5. –
С.465-500