牛顿插值

牛顿插值法的递归实现(C++)

示例
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#include <iostream>
#include <vector>
using namespace std;
double yFunc(double x);
double diff_quotient(vector<double> xi, vector<double> yi);

int main(int argc, const char * argv[]) {
    cout<<"请输入插值的次数"<<endl;
    int t;
    cin>>t;
    double m;
    cout<<"请输入待估计的x"<<endl;
    cin>>m;
    vector<double> x;
    vector<double> y;
    double temp;
    for (int i = 0; i <= t; i++) {
        cout<<"请每次输入一个插值节点"<<endl;
        cin>>temp;
        x.push_back(temp);
    }
    for (double i : x) {
        y.push_back(yFunc(i));
    }
    double result = 0;
    for (int i = 0; i <= t; ++i) {
        double w = 1;
        for (int j = 0; j < (x.size() - 1); ++j) {
            w *= (m - x[j]);
        }
        result += diff_quotient(x, y) * w;
        x.pop_back();
        y.pop_back();
    }
    cout<<result<<endl;
    return 0;
}

double diff_quotient(vector<double> xi, vector<double> yi){
    if (yi.size() == 1) {
        return yi[0];
    }
    else{
        vector<double> slicex, slicey;
        for (int i = 1; i < xi.size(); ++i) {
            slicex.push_back(xi[i]);
            slicey.push_back(yi[i]);
        }
        vector<double> slice_x, slice_y;
        for (int i = 0; i < (xi.size()-1); ++i) {
            slice_x.push_back(xi[i]);
            slice_y.push_back(yi[i]);
        }
        double re;
        re = (diff_quotient(slicex, slicey) - diff_quotient(slice_x, slice_y))/(xi[xi.size()-1] - xi[0]);
        return re;
    }
}

double yFunc(double x){
    double re = sqrt(x);
    return re;
}