xi4
3(x xi 1)2(hi 2x 2xi)hixi 14
3(x xi)2(hi 2x 2xi 1)hi
4xi
(x xi 1)2(x xi)2hi
3
4xi 13
2(x xi)2(x xi 1)hi
误差为
f(x) Ih(x)
1(4)
f( )(x xi)2(x xi 1)2 4!1h maxf(4)( )(i)424a x b2
又 f(x) x4
f(4)(x) 4! 24
hi4h4
maxf(x) Ih(x) max a x b0 i n 11616
试求三次样条插值，并满足条件：
(1)S (0.25) 1.0000,S (0.53) 0.6868;
(2)S (0.25) S (0.53) 0.
解：
h0 x1 x0 0.05h1 x2 x1 0.09h2 x3 x2 0.06h3 x4 x3 0.08 j 1
hj 1hj 1 hj
, j
hjhj 1 hj
533
, 2 , 3 , 4 11457