1
924
, 2 , 3 , 0 11457
f(x1) f(x0)
f x0,x1 0.9540
x1 x0f x1,x2 0.8533f x2,x3 0.7717f x3,x4 0.7150
(1)S (x0) 1.0000,S (x4) 0.6868d0
6
(f x1,x2 f0 ) 5.5200h0
f x1,x2 f x0,x1
4.3157
h0 h1
d1 6
f x2,x3 f x1,x2
d2 6 3.2640
h1 h2
f x3,x4 f x2,x3 d3 6 2.4300
h2 h3d4
6
(f4 f x3,x4 ) 2.1150h3
由此得矩阵形式的方程组为
2 1 M0 5.5200
59 2 M1 4.3157 1414
32
2 M2 3.2640
55
34
2 M3 2.4300
77
1 2 M4 2.1150
求解此方程组得
M0 2.0278,M1 1.4643
M2 1.0313,M3 0.8070,M4 0.6539
三次样条表达式为 S(x) Mj (yj
(xj 1 x)3
6hj
2
Mj 1
(x xj)3
6hjMj 1hj
6
2
Mjhj
6
)
xj 1 xhj
(yj 1
)
x xjhj
(j 0,1, ,n 1)
将M0,M1,M2,M3,M4代入得