f (x 0), f (x 1), f (xn) - (n +1) y=f (x), [ a, b ], x 0, x 1, , xn. y=f (x) xk = kh (k =0,1,, n) .
1. :
k - ( , i= 0,1,2,.., n).
.
Pn (x) :
(1)
n +1 n +1 (i =0,1,, n) : i =0, x = x 0, , , , 0 = 0.
, i =1
0 = 0. 1 .
i =2 : : .
, k : ( , ). (1)
. (2)
.
, , , (2) . . q, : , . :
(3)
2. , ( , ).
, , - , (3) , x, (3) . (. .), , , .
, , (3), . , (1), , : , ,
|
|
(4)
n +1 (i =0,1,, n) , . x = xn, x = xn- 1, , x = x 1 :
,
, ,
,
.
: ( , ). (*)
(5)
xn , yn .
, q, : (5) . :
(6)
.
3. , , xn.