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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]*n24 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 = 111         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)

 

关于拉格朗日和内维尔插值算法的python实现