def diff(xi,yi,n): ''' param xi:插值節點xi param yi:插值節點yi param n: 求幾階差商 return: n階差商 ''' if len(xi) != len(yi): #xi和yi必須保證長度一致return else:diff_quot = [[] for i in range(n)]for j in range(1,n+1): if j == 1:for i in range(n+1-j): diff_quot[j-1].append((yi[i]-yi[i+1]) / (xi[i] - xi[i + 1])) else:for i in range(n+1-j): diff_quot[j-1].append((diff_quot[j-2][i]-diff_quot[j-2][i+1]) / (xi[i] - xi[i + j])) return diff_quot

測試一下：

xi = [1.615,1.634,1.702,1.828]yi = [2.41450,2.46259,2.65271,3.03035]n = 3print(diff(xi,yi,n))

返回的差商結果為：

[[2.53105263157897, 2.7958823529411716, 2.997142857142854], [3.0440197857724347, 1.0374252793901158], [-9.420631485362996]]

def Newton(x): f = yi[0] v = [] r = 1 for i in range(n):r *= (x - xi[i])v.append(r)f += diff_quot[i][0] * v[i] return f

測試一下：

x = 1.682print(Newton(x))

結果為：

2.5944760289639732

def Newton(xi,yi,n,x): ''' param xi:插值節點xi param yi:插值節點yi param n: 求幾階差商 param x: 代求近似值 return: n階差商 ''' if len(xi) != len(yi): #xi和yi必須保證長度一致return else:diff_quot = [[] for i in range(n)]for j in range(1,n+1): if j == 1:for i in range(n+1-j): diff_quot[j-1].append((yi[i]-yi[i+1]) / (xi[i] - xi[i + 1])) else:for i in range(n+1-j): diff_quot[j-1].append((diff_quot[j-2][i]-diff_quot[j-2][i+1]) / (xi[i] - xi[i + j])) print(diff_quot)f = yi[0] v = [] r = 1 for i in range(n):r *= (x - xi[i])v.append(r)f += diff_quot[i][0] * v[i] return f

到此這篇關于用Python實現牛頓插值法的文章就介紹到這了,更多相關python牛頓插值法內容請搜索好吧啦網以前的文章或繼續瀏覽下面的相關文章希望大家以后多多支持好吧啦網！