关于拉格朗日和内维尔插值算法的python实现

先是逐步插值，主体十分简单，关键在于算法部分，我运用了矩阵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):
 8     y = 0
 9     for i in range(3):
10         t = 1
11         for j in range(3):
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)