.
. ,
.
x 0 [ a, b ].
x k (k = 0, 1, 2,...) , x . k - (xk)
, ,
, , .
, .
φ (x) [ a, b ]. :
,
δ δ , . , δ δ . ε ε .
, x k (k = 0, 1, 2,...) x . , . ε . , , ε k ,
,
.
.2. .3.
.
.2, [ a, b ] x 0 j (x 0). y = x x 1. , x 2, x 3,..., x k,... , . . .3 , . x k x . f (x) = 0 x = j (x).
, f (x) = 0 , . , x = x + λ f (x), λ , , j (x) = x + λ f (x).
|
|
x 3 7.3 x 2 + 16.8 x 12.2 = 0,
[1, 2] .
,
f (1.0) = 1.03 7.31.02 + 16.81.0 12.2 = 1.70,
f (1.5) = 1.53 7.31.52 + 16.81.5 12.2 = 0.05,
f (2.0) = 2.03 7.32.02 + 16.82.0 12.2 = 0.20.
.4, x 0= 1.5. ,
x = x + λ (x 3 7.3 x 2 + 16.8 x 12.2),
φ (x) = x + λ (x 3 7.3 x 2 + 16.8 x 12.2),
= 1+ λ (3 x 2 14.6 x + 16.8),
λ.
.
ࠠ 1 < 1 + 1.65 λ < 1,
2 < 1.65 λ < 0,
1.212 < λ < 0,
λ = 0.6.
x 0 = 1.5
x 1 = 1.5 0.6(1.537.31.52 + 16.81.5 12.2) = 1.53.
x 2 = 1.53 0.6(1.5337.31.532 + 16.81.53 12.2) = 1.5318,
x 3 = 1.5320, x 4 = 1.53202.