多项式最小二乘插值法 c++

这是一个多项式最小二乘插值法的C语言实现：

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define MAX_N 100
#define MAX_M 10

double x[MAX_N], y[MAX_N];
double a[MAX_M], b[MAX_M], c[MAX_M];

int main()
{
    int n, m, i, j, k;
    double sum, t;

    printf("Please input the number of points n (1 <= n <= %d): ", MAX_N);
    scanf("%d", &n);
    printf("Please input the points x and y:\n");
    for (i = 0; i < n; i++)
        scanf("%lf%lf", &x[i], &y[i]);

    printf("Please input the degree of the polynomial m (1 <= m <= %d): ", MAX_M - 1);
    scanf("%d", &m);

    for (i = 0; i <= m; i++) {
        sum = 0.0;
        for (j = 0; j < n; j++)
            sum += pow(x[j], i) * y[j];
        a[i] = sum;

        for (j = 0; j <= m; j++) {
            sum = 0.0;
            for (k = 0; k < n; k++)
                sum += pow(x[k], i + j);
            b[i * (m + 1) + j] = sum;
        }
    }

    for (i = 0; i <= m; i++) {
        for (j = i; j <= m; j++) {
            sum = 0.0;
            for (k = 0; k < n; k++)
                sum += pow(x[k], i + j);
            c[i * (m + 1) + j] = sum;
            c[j * (m + 1) + i] = sum;
        }
    }

    for (i = 0; i <= m; i++) {
        for (j = i + 1; j <= m; j++) {
            t = c[j * (m + 1) + i] / c[i * (m + 1) + i];
            for (k = i; k <= m + 1; k++)
                c[j * (m + 1) + k] -= t * c[i * (m + 1) + k];
            b[j * (m + 1) + m + 1] -= t * b[i * (m + 1) + m + 1];
        }
    }

    for (i = m; i >= 0; i--) {
        sum = 0.0;
        for (j = i + 1; j <= m; j++)
            sum += a[j] * c[i * (m + 1) + j];
        a[i] = (b[i * (m + 1) + m + 1] - sum) / c[i * (m + 1) + i];
    }

    printf("The coefficients of the polynomial are:\n");
    for (i = 0; i <= m; i++)
        printf("a%d = %lf\n", i, a[i]);

    return 0;
}

代码中使用了一个二维数组c来存储矩阵，并使用了高斯-约旦消元法求解线性方程组。输入时需要先输入点的个数和坐标，再输入多项式的阶数。输出时将多项式的系数输出即可。