曲线拟合

首先根据已知点的分布判断是几阶函数，再拟合出各次项系数。

c++代码如下:

#include "math.h"
#include "stdio.h"
#define N 7

int main(){
	float a[10][10], x[N + 1], y[N + 1], s, t[10], d, t1;
	int i, j, k, m = 2, l;   //m为阶数
	for(i=1;i<=N;i++){
		   scanf("%f %f",&x[i],&y[i]);
	   }
	   scanf("%d",&m);
	for (i = 0; i <= m; i++){
		s = 0;
		for (k = 1; k <= N; k++)
			s = s + pow(x[k], i)*y[k];
		a[i][m + 1] = s;
		for (j = 0; j <= m; j++){
			s = 0;
			for (k = 1; k <= N; k++)
				s = s + pow(x[k], i + j);
			a[i][j] = s;
		}
	}
	for (i = 0; i <= m; i++){
		for (j = 0; j <= m; j++)
			printf("%f", a[i][j]);
		printf("\n");
	}
    //列主元高斯消去法求解线性方程组
	for (k = 0; k<m; k++)   
	{
		d = a[k][k];
		l = k;
		for (i = k + 1; i <= m; i++){
			if (a[i][k]>a[l][k]){ d = a[i][k]; l = i; }
		}

		if (fabs(d)<1e-6){
			printf("data error"); break;
		}
		if (l != k){
			for (j = k; j <= m + 1; j++){
				t1 = a[l][j]; a[l][j] = a[k][j]; a[k][j] = t1;
			}
		}
		for (i = k + 1; i <= m; i++){
			a[i][k] = a[i][k] / a[k][k];
		}
		for (i = k + 1; i <= m; i++)
		for (j = k + 1; j <= m + 1; j++)
			a[i][j] = a[i][j] - a[k][j] * a[i][k];
	}
	for (k = m; k >= 0; k--){
		s = 0;
		for (j = k + 1; j <= m; j++)
			s = s + a[k][j] * t[j];
		t[k] = (a[k][m + 1] - s) / a[k][k];
	}
	printf("%f", t[0]);
	for (i = 1; i <= m; i++){
		if (t[i]>0) printf("+");
		printf("%f*x^%d", t[i], i);
	}
	return 0;
}