F(X) , , , ..
F(X) = F1(x1) + F2 (x2) + + Fn (xn) (8.9)
( , Fj(xj) = 0 j).
(8.7), (8.8) Z, φi . : ()
(8.10)
- , fi φij , . , , .
, .
- h(x) , [0, a]. r x0 < x1 < < xr , x0=0, xr=a (. 8.2). hk(x) (k=0, , r) . (xk, hk) (xk+1, hk+1) . h(x) [0, a].
(xk, hk) (xk+1, hk+1) ( ). λ, :
x= λxk+1 + (1- λ)xk,
= λhk+1 + (1-λ)hk 0 ≤ λ ≤ 1 (8.11)
, x [ xk, xk+1 ] λ, (8.11). 1- λ = λk, λ= λk+1, (8.10) :
x= λk xk + λ k+1 xk+1,
= λk hk + λ k+1 hk+1 (8.12)
λk + λ k+1=1, λk ≥0, λ k+1≥0.
, x [ 0, a ] :
λk ≥ 0, (k=0, ,r) (8.13)
λk ( k- ) ( ).
, , , ( ) xj. xjk (8.13) - fi φi j. (8.10) :
(8.14)
xj ≥ 0, j=1, 2, , n
(8.14) ( ).
8.5.......
. , , , , . (.. ) .
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