[ a;b ] n+ 1 x: x 0, x 1,, xn y=f(x): f(x 0 )=y 0, f(x 1 )=y 1, f(xn)=yn. , , , .. Ln(xi)=yi i=1,n
;
,
Li(n) - .
, , .
, yi, .
.
n= 1
n= 1 2 : (x 0; y 0 ) (x 1; y 1 ).
, -
n= 2 (x 0; y 0 ), (x 1; y 1 ), (x 2; y 2 )
:
L 3 (x)=x 3 +x 2 -x+ 2
:
x-x0 | x0-x1 | x0-x2 | .. | x0-xn |
x1-x0 | x-x1 | x1-x2 | .. | x1-xn |
x2-x0 | x2-x1 | x-x2 | .. | x2-x1 |
.. | .. | .. | .. | .. |
xn-x0 | xn-x1 | xn-x2 | .. | x-xn |
i - Di, n+ 1 (x). , :
n+1(x)=(x-x 0 )(x-x 1 )(x-xn)
i=1,n
( ),
x= at+b
xj= atj+b j=0,n
Li(n)(x)= Li(n)(t)
Ln(x), x, :
:
..
:
Xi | Yi | Xi-X | Li-1,i | Li-2,i-1,i | Li-3,i-2,i-1,i |
X0 | Y0 | X0-X | L01 | L012 | L0123 |
X1 | Y1 | X1-X | L12 | L123 | L1234 |
X2 | Y2 | X2-X | L23 | L234 | |
X3 | Y3 | X3-X | L34 | ||
X4 | Y4 | X4-X |
, L 01 n(x) L 01 n(n+ 1 ) .
.. , .
: x= 27, =0,1
i | xi | yi | xi-x | Li-1,i | Li-2,i-1,i | Li-3,i-2,i-1,i | Li-4,i-3,i-2,i-1,i |
68,7 | -13 | 48,33 | 49,38 | 49,31 | |||
64,0 | -10 | 49,71 | 49,26 | ||||
44,0 | 48,90 | 48,21 | |||||
39,1 | 50,46 | ||||||
32,0 |
|
|
, .. , .
,
-
-
-
-
- -
-
1- | 2- | 3- | 4- | |||||
-
-
:
1- | 2- | 3- | ||
1,450 | ||||
1,127 | ||||
1,5 | 3,140 | -0,098 | ||
0,795 | - 0,012 | |||
3,4 | 4,650 | -0,18 | ||
-0,159 | ||||
6,8 | 4,110 |
-
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