. - .
. 0,95 0, 98.
, .
, , , .
, , .
, , . , , , .
, , , , , , , .
2.1.1. .
y = f(x, a0, a1,.., am) ei = f(xi, a0, a1,.., am) yi (x yi). a0, a1,.., am , ,
(2.1)
, :
(2.2)
f(x, a0, a1,.., am) , (2.2) . :
(2.3)
,
(2.4)
(2.3) :
(2.5)
y = a0 + a1x, (2.6)
:
(2.7)
. , (2.7), . 2.1.
|
|
2.1.
(2.7)
xi | yi | xiyi | xi2 | |
X1 | y1 | x1 y1 | x12 | |
X2 | y2 | x2 y2 | x22 | |
n | xn | yn | xn yn | xn2 |
,
(2.8)
:
(2.9)
, (2.9), , . 2.2.
2.2.
(2.9)
xi | yi | xi2 | xi3 | xi4 | xiyi | xi2yi | |
x1 | y1 | x12 | x13 | x14 | x1y1 | x12 y1 | |
x2 | y2 | x22 | x23 | x24 | x2y2 | x22 y2 | |
. | . | . | . | . | . | . | . |
. | . | . | . | . | . | . | . |
. | . | . | . | . | . | . | . |
n | xn | yn | xn2 | xn3 | xn4 | xnyn | xn2yn |
(2.5), (2.7), (2.9) , . .
2.1.2. .
, , , , . . , . , , , , . .
n m m+1 a0, a1, ,am, , m<n.
, x, , .
(2.10)
j0(x) = 1, j1(x) = x + a1, , jm(x) = x + am,
j1(x) l
(2.11)
, .
, - , a0, a1, ,am. (2.1). :
(2.12)
(2.12) j0(x),, jm(x) , :
(2.13)
, x1, x2, , xn jl(x) . . (2.12) , :
(2.14)
(2.13), , j0(x) = 1 l = 0, k = 1 j1(x), :
|
|
(2.15)
(2.11)
j1(x) = x + a1,
(2.15) :
(2.16)
(2.17)
(2.18)
j2(x) (2.13) l = 0, k = 2 l = 1, k = 2, :
(2.19)
j2(x) , .
j2(x) = (x + b2)j1(x) + g2j0(x). (2.20)
(2.20) (2.19), , j0(x) = 1,
(2.21)
(2.15)
(2.22)
(2.22), :
(2.23)
b 2 g 2, j2(x) (2.20).
b 2 g 2 (2.23)
(2.24)
(2.24) , å j1(x) = 0.
, j0(x), j1(x), j2(x) . (2.14) a 0, a 1, , a m. (2.10) , j0(x),, jm(x) a 0, , a m , , am+1 j m+1(x). , (2.20) (2.22), jm+1(x) (2.24) am+1.
2.1.3. .
. :
y(m+1) = (1-α)*ym+(1-α)α*ym-1+(1-α)α2*ym-2+(1-α)αk*ym-k (2.25)
y(m+1 ) - ;
α - , 0< <1;
ym-k - , .
α :
(2.26)
m - , (m ≥ 2).
, . .
- . - . 14- , 13- ...
2.1.4. .
.
y(m+1) =(ym+ym-1+ym-2+ ym-3+ym-4)/5 (2.27)
2.2. .
:
12 :
:
0,98 0,95.
, . . .