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mo VA 'x'^UITG IDC CHUYEN NCaHiiP

M -van BO

GAO tjjfa DUNG ( ^ csiuiro
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Ha-nOl. - 1978
B03K)3roi£03£O3fi02eO3ro2©2tO3*O3»KO3EOKO3e03»r«)3£O2fi03eO3©3^

C^^ctofa: haj. 5 M$t v a i phi:?cmg phap ngi suy tSng qu5t
svQT T§ng d | g i a i gin dung phtfcmg trinli
tofin tiJ
g o D^t v8n etS

45

i 1 M§t v a i kiaai nlga ve cSng thrJo n§i suy Tfiu-tcm
si^y rOng

i^

§2

"VS ffiOt v a i pbucng phSp n§i s^y tong quat s i ^
rgng g i a i gSn dung phu^c?ng t r i n h toan tiJ va
si; h $ l t v cua n6
. • • •

Gfaifgya;;!^ l?a

t Ph8n iJng d^ng

i 1 Mgt s5 T^ag d\wig cho 3191 v a i to^n ti> cy thS
1.1 Phi?c?n6 t r i n h haci thi/c vo^ bi§n s8 thi;c
1^2 H$ phtfc^ng t r i n h dgii sfi p h i tuySn hc$c
siSu v l ^ t
1.5
i 2


•vf dy nhu^ dpi s5 t^iySn t i n h , phu'C^ng t r i n h v i p h a n , phutmg
irinh t l c h p h a n , g i a i t l c h p h i tuyen v . v . . . *
TThieu l o ^ i h a i toan k h a c nhau oou eo che v i 3 t du&i
l?ng chiing
(1)

Ax

=

0,

t r o n g do A l u t o a n t u xac d^nh t r o n g ngz khong g i a n noo do
va CO g i a t r t t r o n g mgt khong i;ian cung l o ^ i .
DS g i a i gan dung phu^c-rig' t r i n h ( 1 ) ngi;?o'i t a dung n h i e u
phi?o'ng phap k h £ c nhau. L.oi phv.Xi^r^'; phap dou oo nhu'ng 'J*ii (Tien
va nhu-ng hgin che n h a t d i n h . 2n?o'ng hg»p A l a t o a n tu' tuy3n
t i n h , cac k e t quo ve g i a i ;;Sn dmux, da duvc : Gratnoxenxki / f I G j , Otcga F"Mj^
Moctmic / " I B J T va
n h i e u cong t r i n h (Tu^g^c a>ng b6 tror_g cue t^^ c h i to.4n hgc k h a c
nhau / " J - 1 ^ 7 , / f 2 1 - > 2 7 .
Trong ban l u y n vun nay chung t o i se t r i n h bay mgt s6
?o'ng Bjii h g c l o n g
hfi'p "^a-ngi l';?76 va ia$t oh'&n da dug^c cong b6 t r o n g / " 5 5 - 5 5 7 »

Tac g i a x i n chan thanh can o'n dor^g chi -"oang dll'c ITgijye]
da dgc ky lu'^ng ban tiiao va cho n h i e u y k i e n dong gop q u i ban
Dgic bi^^t, t a c g i a x i n chan thanli c^:a o'n d3ng chi Phan van ^^p
da da x u a t ^phucfxux; hu'o'ng, da cho n h i e u y k i ^ n dong gop q u i b a
t r o n g c5 qua t r i n h hoan thanh ban l u g n v2.n n a y .


^ e X,

(i ^ 0 , 1 ) .

D6i v c i nhu'ng -xyYian x,-^^ x^ , ( i = 0 , 1 ) ,

o5 d3.rih tn?ng X


tu

( i = oT^

j o i v(?i c5c phSn ti: x ^ , ( i = 0 , 2 ) o5 ^^nh t^x^ng X t h i
A(x , X | , Xp) l a n g t t o a n tu LzonQ tuySn l a n h .
Toan tl? so.ng- tuy-Sn t i n h

ACX^, :20: , s>^) t h o a nan *iou

kign ;
(1.2)

ACx^, x ^ , x^) (x;^ - 3ii) ^ A ( X Q , X;^) - A ( X Q , X . ) ,

di^c ^ i

l a t y s a i phan b-v^c h a i cua han trOYi tJ'g'ng Ax i S y

cac phSn tir x^ ^ X,

( i = 0,2 ) .

tgi


B^a vao ( 1 . 0 ,

t'^ ('1.2) (cau k ^ i •-?, d-g^c -coc dyng ^:ji


(I A(x^, : c . ) | U
0

^

V'^J
6 ^

»

^ -

:.^ . ^

(x.

-:c„),

1

|A(.:^, ::,, x.)|| ^ (-^) II A \ | 1 .
O

i.

(k)

A ( ^ . ^^1



...,

(4-^0)-

JL-^(,o_^^).

T-JP (2.2) suy ra :
(2.3)

A(xg, x ^ , . . . , ^^) ( : ^ » x j ) ( x | - ^ ) . , ,
:= ( ^ " '^ ),!

,k-l

t r o n s d

=

k(k-l)... (k-i M )
i!

L'^t khac, cung d^a vao dj.nh nGhia cua ty s a i phan suy r9ns
b | c k dio toan ti? va dieu ki^>n ( 2 . 2 ) t a I p i co :
(2.5)

Ax - /.x° - l b , k (x - x°) - 'lx° (x - x ° ) g ° =
X

=

AZIQSQ

. . . ( k - D ^ (x - x*^) (x - - i ^ ) . - . (x - 2g_.^)

trong dc5
k-S
'te° = Z (-1)^ cf. o Aoi„(if-l),, Ho'
'O
i=1
+

k-3
>• (-1)^ C^_, A0i„(i+1)„ ( i ^ 2 ) ^ ( ^ - ^ % ) +
i=1



- '

k
/ _L«

3^p

} A xi^+ t ( x - x"^) n i»

0 ; ^ t
1=1
= (-1)

k-1

iAo^

^ - ^ , ,i-(v-0
,
r L (-1)
C^^-^ Ao(k-l)Q
i=1
1^ _r>

k-1

( 2 . 1 6 ) ai,,ic = C - ^ r "

.

-

V- r ^ r ^

Ao1^(I•^Ao1o ./^^-'^^

'^r.i

^ ^


v.'l

Vn.

Lhl do qu5 t r i n h Igp ( 2 . y ) GO !^;i "cy t o i n-ghl^^n x"^ cri.a (1 )
l o e dg hgi ty d-u
* II I^ik II II \ ( ^ . ^ ) I) •

Dya vao cac dieu kipn ciia d^nh l y va c5c bSt dang thu*c ( 2 . 1 8 ) ,
( 2 . 1 1 ) , tii* b a t dong thu'c cu5i cung suy ra dieu p h a i c^iihig
minh. I^u khdng gi5 t h i e t trx^&o ve ay.' tSn t ^ i n g h i ^

cua

phi?cmg t r i n h ( 1 ) , ta co cac dinh l y sau day «
Dinh l y 2 . ?
Gih sv? X thoa nan cac dieu kiyn :
1^/ Toan tiJ To,k tSn t g i toan tu' nghidi dao
-1
va

fJTo,k ll

2^/

-4

To,k

Bo ;

\\Ak

iLcL^ 4 I^i

f
o'

^ LT/^*

( i - o,k-*l).

Kiem t r a d i e u k i e n 1 .
^
^
^
^
-1
l'rL?o'c t i o n t a can ch'Jng n i n h t e n t ^ l t o a n tu* n g h i c h dao T^ ^
Thft v g y , x e t t
—1
(2.26)

||TO,V

(To,:.c-2:i,k) II 4

—1
II To^k |l II I o , k " Ti ,3, ([ =


- 19 k-1

-1
To,k

2Z (-1) i


t o n t g i va

. 0 ,

Dieu kiOn 1 da kiem t r a xong.
KiSm t r a d i § u k i p n 3«
CSn dsnh g i a fl C, ,]r Ax^||
V ^ n = 0 va X = X , d'^a \'ao ( 2 . 9 ) , tt? ( 2 . 8 ) t a ST:y ra :

Ax
Do d6

•^

^ - ^ ^Ic ^

-^
o^

Ck
o


- 20

(2.27)

j j < i , Ax-^ll


"o^

.

De dang chi?ng lainh du^c ??lnn;t nsu / \ l a n g h i ^ ciia phtJWng
trinii (2.23) t h i

A= ('^'^ ^j, ^ ^\^-^

y\""^) - V

Do do t'Jf (2.28) suy ra :

(^.29)

ll ^ \ Ax^ ^^ X, ^ lY^ .r^

=

\

Dieu kign 5 da diro'c chu'ng minh xong.
Cung t'JP (2.29) ta 3uy ra :
(2.50)

f^

:-

2B^ L^
i

—^—

''. + '

>

0

Dieu klgn 2 d i dxJg'c kiem t r a 2X>ng.
Th;/c hifn phep ch^Jng minh hoan toan ti?o'*ng tg?, t a co
the Chiang minh di?g'c cho tr^.?o»ns hgp tSng quat khi chi:Qren ti?
phSn t^ x^"" sang phSn tiJ x^. Tif phep chiJng minh do ta xac
dinh ^ ) | i|x--x^f'4.
- t ( x - - x ^ )


- 25 k-1

4

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