已给sin0.32=0.314567，sin0.34=0.333487，sin0.36=0.352274，计算sin0.3367的值
#include <iostream>
#include<iomanip>
#include <cmath>
using namespace std;
int main()
{
double numerator_cofficient; //用来记录插值分子的乘积结果
double denominator_coefficient; //用来记录插值分母乘积的结果
double input_x; //需要输入的x的值
double x[3]={0.32,0.34,0.36}; //已知x的值
double y[3]={0.314567,0.333487,0.352274}; //已知y的值
double result=0; //用来记录插值结果
cout<<"通过拟合得到的拉格朗日多项式为："<<endl;
for (int i=0;i<3;i++)
{
denominator_coefficient=1;
cout<<y[i]<<"*";
for (int j=0;j<3;j++)
{
if (i==j)
continue;
cout<<"("<<"x-"<<x[j]<<")";
}
cout<<"/";
for (int j=0;j<3;j++)
{
if (i==j)
continue;
denominator_coefficient*=(x[i]-x[j]);
}
cout<<denominator_coefficient<<"*"<<"("<<"x-"<<x[i]<<")";
if (i<3)
{
cout<<"+";
}
}
cout<<endl;
cout<<"请输入需要插值的x:";
cin>>input_x;
for (int i=0;i<3;i++)
{
numerator_cofficient=1;
denominator_coefficient=1;
for (int j=0;j<3;j++)
{
if (i==j)
continue;
numerator_cofficient*=(input_x-x[j]);
}
for (int j=0;j<3;j++)
{
if (i==j)
continue;
denominator_coefficient*=(x[i]-x[j]);
}
result+=(y[i]*numerator_cofficient/denominator_coefficient);
}
cout<<"插值结果为："<<setiosflags(ios::fixed)<<setprecision(10)<<result<<endl;
cout<<"函数的真实值："<<sin(0.3367)<<endl;
cout<<"计算误差为："<<100*(abs(result-sin(0.3367))/sin(0.3367))<<"%"<<endl;
return 0;
}
