拉格朗日插值法

python代码实现插值拟合 1／（1+25x^2)

import matplotlib.pyplot as pltimport numpy as npdef f(x):    return 1/(1+x**2)def L(x, X, Y1):    Ln = 0.0000    t = 0    for j in X:        Molecule = 1.0000        Denominator = 1.0000        for i in X:             if i != j:                 Molecule *= x-i                 Denominator *= j-i        k = Molecule/Denominator        Ln += Y1[t] * k        t+=1    return LnX = np.arange(-5,5,0.5)X1 = np.arange(-5,5,0.1)Y = f(X)Y1 = f(X1)Y2 = L(X1, X, Y)print(Y1)print(Y2)fig = plt.figure(figsize=(8,8))ax = fig.add_subplot(111)ax.set_ylim(-5,5)ax.set_xlim(-5,5)ax.plot(X1, Y1)ax.plot(X1, Y2)plt.show()

图结果

两边的差距过大的现象成为龙格现象。解决方案是分段插值