, f [a, b] , .. g, [a, b]. g - [a, b].
- . , f(x) [0, 1]
x | 1/6 | 1/3 | 1/2 | 2/3 | 5/6 | ||
f(x) |
[0, 1/3], [1/3, 2/3], [2/3, 1]; :
g,
- [0, 1] f ; g [0, 1/3], [1/3, 2/3], [2/3, 1]. 3.2.
3.2
f g. f(x) [0, 1]. [0, 1/3], [1/3, 2/3] [2/3, 1] (|f(x)-g(x)| £ M× hn+1), h = 1/6 n = 2.
.
. , , , h . , 2 , , .. .
, - , , . . n = 4, Ii = [xi, xi+1] - (i = 1,2,3)
3.3 -
i = 1, 2, 3.
q {yi},
q1(x1) = y1, q1(x2) = y2
q2(x2) = y2, q2(x3) = y3
q3(x3) = y3, q3(x4) = y4
, , , g ,
q q1, q2, q3. 8 . q, ,
d1 .
qi, , , .
, , , , , . - . - (x), :
|
|
1. (x) ;
2. (x) Ii = [xi, xi+1], i = 1, 2, ¼, n-1;
3. (x) .
. , .
Ii (x)
i(x) = ai3x3 + ai2x2+ ai1x + ai0, xÎ Ii.
"" n 1 , 4 , 4n - 4 ij.
I. , (.. n 2 ).
, 3(n - 2) = 3n - 6 :
, i = 2, ¼, n - 1.
, (4n 4) 3(n-2) = n+2 .
, (x)
(xi) = yi, i = 1, ¼, n,
n .
. , ,
, , .
, f(x) j(x) f(x) , . . f(x) f(x), , , .. .
p(x) , . p(x) , .
, , , f(x), .