test1源.cpp

#include <iostream>
#include <vector>

// 定义原始函数
double f(double x) {
    return 1 / (1 + x * x);
}

// 定义二次插值函数
double quadratic_interpolation(double x, double x0, double x1, double x2, double y0, double y1, double y2) {
    return y0 * (x - x1) * (x - x2) / ((x0 - x1) * (x0 - x2)) + y1 * (x - x0) * (x - x2) / ((x1 - x0) * (x1 - x2)) + y2 * (x - x0) * (x - x1) / ((x2 - x0) * (x2 - x1));
}

int main() {
    int n = 10;  // 区间数
    int N_values[] = { 10, 20 };  // 不同的N值

    for (int k = 0; k < 2; k++) {
        int N = N_values[k];
        std::vector<double> x_values(N+1);
        std::vector<double> interpolated_values(N+1);

        for (int i = 0; i <= N; i++) {
            x_values[i] = -5 + i * 10.0 / N;
        }

        for (int i = 0; i < N; i++) {
            double x = x_values[i];
            int j = i * n / N;  // 确定所在区间
            double x0 = -5 + j * 10.0 / n;
            double x1 = -5 + (j + 1) * 10.0 / n;
            double x2 = -5 + (j + 2) * 10.0 / n;
            double y0 = f(x0);
            double y1 = f(x1);
            double y2 = f(x2);
            interpolated_values[i] = quadratic_interpolation(x, x0, x1, x2, y0, y1, y2);
        }

        std::cout << "N=" << N << " 时的插值结果：" << std::endl;
        for (int i = 0; i < N; i++) {
            std::cout << "x = " << x_values[i] << ",此时值为 " << interpolated_values[i] << std::endl;
        }
    }

    return 0;
}