关于拉格朗日和内维尔插值算法的python实现
系统：windows7 编辑器：eclipse+pydev 环境：python 3.4
先是逐步插值，主体十分简单，关键在于算法部分，我运用了二维数组的数据结构来存储每次迭代后的新值。角标的循环初看可能有些复杂，自己动手走一遍就会很清楚啦
1 #coding=gbk
2 '''
3 Created on 2014-8-31
4
5 @author: Administrator
6 '''
7
8 def Neville(xt,m,n,x):
9 for i in range(1,n):
10 for j in range(1,n):
11 w[i-j][i]=(x-xt[i-j])/(xt[i]-xt[i-j])
12 m[i][j]=m[i-1][j-1]+w[i-j][i]*(m[i][j-1]-m[i-1][j-1])
13 for i in range(n):
14 for j in range(0,i+1):
15 if j%n==0:
16 print("\n")
17 print(' %f' %m[i][j])
18
19 n = int(input('插入节点个数:'))
20 x = float(input('输入x的值:'))
21 m = [[0 for i in range(n)] for j in range(n)] #创建n*n矩阵
22 w = [[0 for i in range(n)] for j in range(n)]
23 xt = [0]*n
24 for i in range(n):
25 m[i][0] = float(input('插入第%d个y值：' %(i+1)))
26 for i in range(n):
27 xt[i] = float(input('插入第%d个x值：' %(i+1)))
28 Neville(xt,m,n,x)
下面的是拉格朗日插值算法，十分简单，分享借鉴。
1 #coding=gbk
2 '''
3 Created on 2014-8-31
4
5 @author: Administrator
6 '''
7 def lagrange(x,xt,yt,n):
8 y = 0
9 for i in range(n):
10 t = 1
11 for j in range(n):
12 if i!=j:
13 t = t*(x-xt[j])/(xt[i]-xt[j])
14 y = y+t*yt[i]
15 print("结果为：%f" %y)
16
17 xt = []
18 yt = []
19 x = float(input("插值x；"))
20 n = int(input("节点数目；"))
21 for i in range(n):
22 xt.append(float(input("第%d个x的值" %(i+1))))
23 for i in range(n):
24 yt.append(float(input("第%d个x的值" %(i+1))))
25
26 lagrange(x,xt,yt,n)
