NKTZI_2010_rus_modul2
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53
3
3.1
3.1.1
, -
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1.# , $ %-
& $ & .
2.( # & & ,
%# , % & ).
3.(wij=0).
4.3 $&, . . # i-j- # j- i- wij=wji.
5.( # & , % % , ) %5 %-
5.
6.3 & $& ) &.
% . 3.1. |
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x1 |
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w12 |
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x2 |
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wN 2 |
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w13 |
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w23 |
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x3 |
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w3N |
w2 N |
w1N |
xN |
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w N 3 |
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% 3.1 – % |
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54
3 ) - ) , . 3.2. $&
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x1 |
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w21= w12 |
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w13 = w31 |
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w43 = |
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2 w24 = w42 |
w34 |
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w23 = w32 |
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% 3.2 – ;$%
< , ) ), $ $ -
, $ $ . 3 & % = 5 & $ - & % $ %5
5 & & &, $
% = $ . &, >
5 # 5 % % $ , ) -
%$% & ), % % -
& &, # , = ) $ .
> , & & -& ( - $ ) % = ( 1, 2, ... )T %, -
$& $ , , -1 +1. @$ %
& ), & - , % % xP(p=1,P). ( )
> & , % & &
), % & % ) %-
, . . y=xP, ) y=(y1, y2,…,y )T - % & & ) . 3 $ & ) -
> &.
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$ ! " ( $%) %5 :
–5 5;
–> ) :
–&$ .
' ($( ). -
$ & % = 5:
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D xiP – i- % % P.
E # % % $ , %$ % -
> & &. ;, $ % - 5 .
*! +), ' " ,-' . /!$ %$% -
$ ( ) % % & & )
yi (0) = xi , |
i=1,N. |
F = $ & )
$ & %.
%0 " ' " " )' 1 ' 1! ' ,. F
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ij y (k) i = 0, |
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& , - |
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% & $& $ & & )
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1, zj |
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(k +1) = f a (zj |
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(k +1)) 0, zj |
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yj |
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) f (•) - ) % 5 %5, !j - & -
).
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G & & $ , &
$& & & ) & ,
– H ( -
$ ). 3 = $ &
%, $H > . I% 5 # " '-! '', % ) % # % % , $ - & & &, , " '-! '', % ) &
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3.1.2 /40 ' , "
# & = )-$% ) H. H, )-
, H % H. D H %-
%, % % %- ( ). E & # $& , % #
> ( $ -
). 3 % H, H 5-
= ), % H 5 = ),
) % ) . J & % $
, # H $% & , -
= = ). K % , # & % % = )$% %5.
G & % %5 (%5-
) & & &, % % % & & - & # & $ & , $ 5
% % . 3-&, %
H, . . # -
. 3-&, $ &
% , $ & &
. ( ), # & $ -
& & . L% &
# = )$% %5
E = |
1 |
wij xi xj + xi Qi |
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i j i |
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) Qi - $ ) i-) ; wij - i-) j-)
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%, $ % 5 %5 % -
) % ) % H
. I % % % $ % $& )$ ,
& ) ) %$
$ 5. F =, % % # % &, & = )$ - % ) H (= )$% &) - & . J & % 5 -
&, = & # & % &.
3.1.2.1 6 ' ' /!$ , "
M %5 % # % % % H % ($
H H, ) $ H). J & >-
& &, $ = )-$% %5 % # ) , . . % & -
& = )$% ) H. @ % & -
# $# # 5. I % % %
5 # -
5, $ $ % $
, = )$% %5 %.
F 5 ) %5 $&
. ( % & $ %, )
& # 5 . < & -
x i i < 0 , $& % & xi !i -
i
# & %. F !i = -
#. F = 5 !i = 0, $ % %-
E = 1 wij xi xj 2 j j i
@$ ) &H # & im - % & m- ) . K ) 5 wij # 5&,
% & (w1ij) # , % (-),
(wim) - % (-
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E = 1 w1ij xi xj 1 wim xi xm 2 i i j 2 i m
F ) & # #
% % , & # , % (- ), %5, - % % & ). K % , $& %5 % ) (-) , -
)
Em = 1 wim xi xm 2 i m
N 5 ) & # =% %-
5
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im i |
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w x x |
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i m |
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K % % % m {-1, 1}, ) ( ()2 >0. G & wim = i (, |
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wim xi xm = (xi)2 (xm)2 |
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i m |
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K % , & wim = i ( $ % %- |
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5 5 5.
3.1.2.2 %$, /!$
F ), % % > & & & -
( = )$% H), 5 # & $ 5 %5 H % - $ . = )$% ) H -
H & = ), 5 = ) - % %- $ .
F = )$% %5 -k & #
E(k) = |
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3 & ) & &
. 3 # (k+1)
% = )$% %5, &$
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j (k +1) + |
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E(k +1) = E(k +1) E(k) = |
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F #, $ (k+1) H -
) m-) ( ) $
), # & & ) . 3 = ) & ) & i=m j=m
% &. L$&, $ wij=0 wim=wjm
i=j (, & # # :
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E(k +1) = wim xi(k +1) xm (k + |
1) + Qm xm (k +1) |
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j m |
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(k) + Qm xm |
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wim xi(k |
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E(k +1) |
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+1) + Qm xm |
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i m |
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wim xi(k) + Qm xm (k) xm |
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i m |
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3 ), $ i m xi(k+1)=xi(k), -$
E(k + 1) = |
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= [zm (k + 1) Qm |
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) xm (k + 1) = xm (k + 1) xm (k ).
F & # &$ E(k +1) # &
$
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1. Z m ( k + 1) > m
E $ , $ m- %, . . &-
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% & &. K % , xm (k + 1) > 0 |
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< 0 . |
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Z m ( k + 1) < m |
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), . . |
xm (k + 1) < 0 , % % % Z m ( k + 1) m < 0 , |
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= )$% %5 % # % H. 3& # $ -
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H = ) &. E % -
% = )$% # - # = )$% ) , . . -
& & ) . < & 5 ) )-
) %, ) % % =%, >
& $ .
K % , . ! 6 4':( ' ! , ' ) "
1. /40 '.
F > & P ( = 1, ). 3&$ = & wij
5& , % & (
"+1") % ) & ) &$ -= ) % # )
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E = |
xip(k +1) wij xpj (k) |
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2 i=1 |
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2. "$' , '.
F > &, #, % # &, = ) &$ & $ & & )-
# $& .
3.1. %5 , -
7 ) %5 % 5
) ! = 0, $ % & 1=(1 -1 -1 1 -1 1 1)+ 2=(-1 -1 1-1 1 -1 1)T % # %-
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# & 3= 2 = (-1 -1 -1 -1 1 -1 1) (% # & $%-
).
.3.3 $& % & V
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w 13 |
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w51 = w15 |
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x5
x6
x7
w57
% 3.3 – , 7
E & wij 5& W 7x7,
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w11 = 0 w12 w13...w17 |
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w21 w22 = 0 w23...w27 |
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W =W |
+W |
= |
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.................... |
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...w77 |
= 0 |
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w71 w72 w73 |
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) Wi - 5 i-) (i=1,2) $) , =-
& % &$ :
w12 = 1 ( 1) + ( 1) ( 1) = 0 |
w13 = 1 ( 1) + ( 1) 1 = 2 |
w14 = 1 1+ ( 1)( 1) = 2 |
w15 = 1 ( 1) + ( 1) 1 = 2 |
w16 = 1 1+ ( 1)( 1) = 2 |
w17 = 1 ( 1) + ( 1) 1 = 0 |
F 5
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00 22 220 |
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000000 2 |
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200 22 20 |
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20 20 220 |
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w = |
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20 22 200 |
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0 200000 |
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3&$ = ) % # ) ,
% % & & )
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= Ei |
= E1 + E4 |
+ E6 |
+ E7 |
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i=1 |
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+)]= |
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[( 2)( 1) + 2 1+ ( 2)( 1) + 2 1]= 4 |
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w43 x3 |
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w45 x5 |
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w46 x6 |
+)]= |
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[2 1+ ( 2)( 1) + ( 2)( 1) + 2 1]= 4 |
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w64 x4 |
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w65 x5 |
+)]= |
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[2 1+ ( 2)( 1) + 2 1+ ( 2)( 1)]= 4 |
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E 17 = 12 [x1 ( w72 x2 )]= 12 [( 2)( 1)]= 1
K )E 1 = -13. I )$ $ )
7
E2 = Ei2 = E32 + E52 + E72 = 9 i=7
3 = 2 $ ) =- ), % )$& &$
7
E 3 = E 3i = E 35 + E 37 = 5 i = 1
3&$ & - $ & & ), % & $ % 5-
%5 &
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z3j = wij x3i , j = 1,7 i=1
z13 = w31x33 +w41x43 +w51x53 +w61x63 =( 2)( 1)+2 ( 1)+( 2) 1+2 ( 1) = 4<0