数值计算第二次大作业r
r
r
验证三次样条函数插值是否有几何不变性r
r
（1）给定的插值条件如下：r
i01234567r
Xi8125849094859699591017102r
Yi0077400990280600708120018002177r
r
端点边界条件为第一类边界条件（给定一阶导数）：r
r
r
Yr
001087r
r
0r
r
r
Y100r
r
7r
r
r
r
三次样条函数的构造过程如下：r
设r
x1r
x2r
x3r
x
1x
共r
个插值节点，则经过数据点r
r
x1y1r
r
x2y2r
x
y
r
的三次样条r
Sr
xr
是一组三次多项式：r
r
r
S231111111112xabxxcxxdxxxxxr
r
r
r
r
r
23r
r
r
r
r
ar
xr
xr
cr
xr
dxr
xxxxr
r
S2x2b22r
2x2r
22r
23r
r
r
r
11r
r
r
r
r
r
Sxr
x3xxxr
r
r
r
r
21111111


xabxxcxxdr
r
r
1
1r
r
r
r
r
由节点处的连续性可知：r
r
r
Sr
xr
ySr
xr
yi12
1r
r
iiiii1i1r
r
ar
yi12
1r
r
iir
r
r
r
r
yy2321121121121bxxcxxdxx12r
r
r
r
r
r
yr
yr
br
xr
xr
cxr
x2r
dxr
x3r
r
r
r

1
1
1
1
1
1
1r
r
由节点处的一阶与二阶光滑性可知：r
r
r
Sir