算法思想：用多项式逼近原函数

import numpy as np
from numpy import *
import numpy.linalg as lg    #numpy的线性代数函数库 linalg
import math
x=[]
y=[]
N=10
pi=math.pi
#形成十个(x,y）点
for i in range(N):
    x.append(round((-1+(2/N)*(N-i)),3))
def function(x1):
    return math.sin(pi*x1)
for i in range(len(x)):
    y.append(function(x[i]))


n = len(x)
X= zeros((n, n))
for i in range(n):
    for j in range(n):
        X[i][j] = math.pow(x[i],j)
print(X)    #范德蒙
A=[]    #系数矩阵
XT=lg.inv(X)  #求X得逆矩阵
Y=zeros((n,1))
for i in range(len(y)):
    Y[i][0]=y[i] 

A=lg.solve(X,Y)    #解系数矩阵
def polynomial_interploate(x1):
    P=0
    for i in range(len(x)):
        P+=A[i][0]*math.pow(x1,i)
    return P