DI nhien la cvc tieu clla Fa tren toaD khong gian X va do do thoa
do 8 =O(Fa)~ l-a ~
do y= e(Fa)~ theo3-5 - 3 ta du'<;fcx~ ~ U
l~i dung (13) ta co :
Ilx~ - till~ l-a +Ilx~ - till ~ 0
(b) do (13): II ~+ ll xa -n il Ilx~ - u ~ Fa m ma a =C8 (00 gia thie't) ~~= J6 & Fa Fe
v~y: IIx~ - nil=eJ6
y=eFa
nenthe03-5-3taco: IIx~ -ull=e(Fa)=eJ8'
(c) : cling do (13) ta co:
IIx~ - nIl~ J-a + Ilx~ - nil
( 2/3 2/3 ) 6 6 62/3 a = C6 ~..Ja = JC61/3 JC y = e( 0 2/3 ) = e (a )
N~n theo 3-5-3 la phai co: IIx~ - ull=e(a)=e(8%J
V?y:
Do gia thi€t :
Do gill:thi€t :
IIx ~ - nil = e( 02 / 3) .
Ta tie'p t~lCxet sit hQi tl,l ye'u cua : x~ 3-5-6. ne) d~ :
_Ne'u a =Clemo)va y=y (mo) tho a y= e(ra) va y E Vkvdi mQtk nao d6 thl:
Clu'tng minh: (xa - x ,A Aya * )-) 0 m m . khi 0-)0 Tu: Vk cVm;Vm~k Ta c6: I(x~ - x~ 'A * Ay)1 = ( A( x~ - x~),Ay)1
= [x~ -x~,y ]-a( x~ -X~,y)1={g-g,Ay)-a(x~ -X~,y)1 ={g-g,Ay)-a(x~ -X~,y)1 ~ j(g- g,Ay ~+al( x~ -X~,y)1
0
~ ollAllllyll+allyll ra
~ o(ra + IIAllJlyl1
(do dinh nghla [.,.])
(do (12))
(do 3-5-4)
Cho 0 -) 0 ta du'Qcdi€u phai chung minh. 3 5 7 n'"d" NA'
- - .~: eu:
.
y= e(ra) 0 = e(ra) va zEkerA khid6 (xa -Xci ,z)-:-+O khi 0-)0m m
Cllll'11g I1linlz: ta dii bie't d (3):
a * 1 * (adsbygoogle = window.adsbygoogle || []).push({});
xm =(Am mA + aT)- Amg
.
Tu'dngtit cho x~ vdi g thay bdig
xa =m (A * Am m + aI)-1 A *mg
tu: (v,A' y)=(A v,y ) VVEV ,YEY
rn TIl m
va (v,A *y)=(Av,y) VvE x va YEY
ta c6:
(v,(A* -A*)y)=O VYEY va VEV (vIA =
j<v )
m m m
m =>(v,A* ,y)=(v,A*y)m VYEY va VEVm
* *
tucla: Am =QmA
QI1I la phep chieu tn1c giao tu X leu vm.
Dodo:
(
xa -XaZ
)=(A* (A* A +aI)-lG~_g),z)
m m m m m
=(QmA*(A* Am m +aI)-lCi~-g),z)
Ma do Z E kerA nen Az= 0
=>(A*(A* Am m+aI)-l(g_g),z)=((A* mAm+aI)-l(g_g),Az)=O VI v~y:
(xa -xaZ )=(Q
.A*(A* A +aI)-l(g_g),z)-(A*(A* A +aI)-l(g_g),z)
m m m mm mm =((Qm -I)A*(A*mAm +aI)-l(g_g),z) Tal~ico: I (Q -I)A*(A* A +aI)-l(g_g),Z) 1 m m m = I
(A* A +aI)-l(g_g),A(Q -I)2Z)
1
m m m
~ ,O,y,II(I-Qm)zll ~ 0 . (adsbygoogle = window.adsbygoogle || []).push({});
Khi m=mo~ CX) .
Bay giG ta xet nguyen 19 phan ky(discrepancy principle) cho tntong hQp hii'llh~n chi€u
Gillsll' gthoa IIg-gll~o<cllgll vdiO<c<l (14)
Ta v~n k9 hi~u Pmla phep chieu tn1c giao clla Y leu A(Vm)
3-5-8.86 de: Gill sll' m c6 djnh va % < lipmgll khi do co duy nha't gia trj a =a(m) sac
cho IIAX~ - Pmgll = ~ . Clui:ng minh : Chli 9r~ng : . II AXa_p g ll = II A xa_p g ll - m m mm m "'?? ,:tll;, ~'"
ta se thu du'Qc ket qua cua bo de tli 3-3-1 bang cach
thay A,gO,otrong 3-3-1 boi cac yeu t6 tuong ling: Am, P g,o/m Ic .
Cho trudc 0 do (14) va (3-5-1) ta luau luan co the chQnm=m(o) sac cho:
~< lipmgll va YlII= 0(0)
3-5-9. 86 de: Neu m = m(o) du'QcchQnthoa(15) va a =a(m(o» thoa IIAX~- Pmgll=~
khi dollx~11~ Ilullkhi 0 dll nho (0 day u=A+g)
Clui:nf.!minh: .
Do xa la cuc lieu Clla Fa lIen Vmta co: Fm . . a (xam)~ F (Qa~m U)
(15)
=>IIAX~- pmgl12 +11(1- Pm)g112 +allx~112
~IIAQmu-t +allQmull2
~ IIAQmu - Pmgll2 +110-P m)g112+alluf
va tu d6:
8~ -IIAQm u - Pmgl12+allx~1I2 ~ allul12 e
tHYnhien bdi (14) va (15)
IIAQmU -Pmgll =lIPID(AQmu- g)1I
~ IIA(Pm - I)ull +8=0(8)+ 8 < ~
Cho 8 all nho ta thu dtiQeke't qua
Chli '1r~ng dtioi cae dieu ki~n eua 3-5-9 ta co:
Jim (Axa -g)= Jim (Axa -P g)=O
8~0 m 8~0 m m
Do d6 e6 th~ dung Bhang 1'1lu~n tu'dngtlf nhti trong 3-3-3 va 3-3-5 d~ thie't I~p cae ke't qua san:
.
3-5-10.Dinh Iv: Trongdieu ki~neu.a3-5-9thl x~ ~ u khi 8~ 0 (adsbygoogle = window.adsbygoogle || []).push({});
3-5-11. Dinh Iv: Gici stl' m=m(8 ) thoa (15); a =a(m(8» thoa 3-5-8