:
ì 1 = 111 + 122 +... + 1nXn + F1
ï 2 = 211 + 222 +... + 2nXn + F2
í............................. (1)
ï
î n = n1խ1 + n22 +... + nnXn + Fn
(E - A)X = F (2),
: eij = 0, e11 = e22 =... = enn = 1;
X = (1,..., Xn)T; F = (F1,..., Fn)T
(E - A T)P = r (3),
: a12T = a21
ì (E - A)X = F ³ FD
í X ³ 0 (4)
î Min(Z), Z = r1X1 + r2X2 +... + rnXn
ì (E - A T)P = r £ r
í P ³ 0 (5)
î Max(Y), Y =FD1P1 + FD2P2 +... +FDnPn
P (E - A)X = P F (6)
(E - A T)P = r (7)
([ ii]+ [ ii])( - - D )( + D) =
= ([ ii]+ [ ii])(F+DF) (8)
([ ii]+ [D ii])( - - D )(+ )=
= ([ ii]+ [D ii])(r+ + ) (9)
[ ii-1][D ii] A T £ £
£[ ii-1]([D ii] A T+[D ii]r) (10),
: = +D; F = F +DF; [ ii-1] , :
1/1 ,..., 1/n ;
D < D; D ¹ D; DFK ¹ DF
- :
å i =(S+K) (11)
:
S/S º 1; (S+K)/(S+K)º 1; i/(S+K)< 1;
0 < S/(S+K)£ 1; - ¥ < (S - %)/(S+K)<1;
K/(S+K)< K% /(S+K);(S - %)/ S < 1
=(P1, P2 ,...,Pn)T=(S+K)(Q1, Q2,..., Qn)T (12)
M /(S+K+DS)=[V ii]( +F)/(S+K+DS)-
-[ ii]( R+r)/(S+K) (13)
(14)
:
h/ N ³ D
:
h/N ³ D(1+N /N)
h / N ³ D (N + N)/ N (15),
: h = ( - )/ ; N = N+N; D .
:
DN £ (N D{h/N} + D(N /N)DN)/ D (16),
D{h/N} .
:
S+K = a (P[]+[] ´ 24 ´ 365)
S+K = CҔ ´ (17)
1 = (CҔ/(S+K))
:
(P1/, P2/,..., Pn/)T =
=(S+K)Q(Q1/Q, Q2/Q ,..., 1,..., Qn /Q)T =
=(S+K)Q(r1,..., r,..., rn)T (18),
: r º 1; /=Q/Q = r/r º 1
:
[ ii](E - A)[ii-1]XP =FP; (E - A P)XP=FP (19),
: aP ij =( i/ j)aij ; F P = [P ii]F ; X P = [P ii]X;
F = [P ii-1]FP; X = [P ii-1]XP
P= A TP+r++ (20)
[ ii](r + + )/(S+K)=
= R /(S+K)£ R/(S+K) (21)
([ ii] A TP+R+"+)/(S+K)£
|
|
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£ ([ ii] A TP+R)/(S+K) (22)
[ ii]r = R = [P ii]FK (23)
C D= F (24)
M=([D ii]( - ) - ([ ii]+[D ii])D ) +
+([ ii]( - -D )+[D ii]( - -D )) - DR (25)
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