数值分析第五版习题总结(14)

6.7593(0.30 x)3 4.8810(x 0.25)3 10.0169(0.30 x) 10.9662(x 0.25)

x 0.25,0.30

2.7117(0.39 x)3 1.9098(x 0.30)3 6.1075(0.39 x) 6.9544(x 0.30) x 0.30,0.39 S(x) 33

2.8647(0.45 x) 2.2422(x 0.39) 10.4186(0.45 x) 10.9662(x 0.39) x 0.39,0.45

1.6817(0.53 x)3 1.3623(x 0.45)3 8.3958(0.53 x) 9.1087(x 0.45) x 0.45,0.53

(2)S (x0) 0,S (x4) 0

d0 2f0 0,d1 4.3157,d2 3.2640

d 2.4300,d

34 2f4 0

0 4 0

由此得矩阵开工的方程组为

M0 M4 0 290

14

32 2 M1 4.3157

55 M

2 3.2640 M3 2.4300

0372

求解此方程组，得

M0 0,M1 1.8809

M2 0.8616,M3 1.0304,M4 0

又 三次样条表达式为

S(x) M(xj 1 x)3

(x xj)3

j6h Mj 1

j

6hjM2

(yM2

jhj

j 1 xj 1hj

j

6

)

xh (yj 1

6

)

x x

jj

hj

将M0,M1,M2,M3,M4代入得

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