/**
* 牛顿插值多项式
* @Author fan_zhang
* @DateTime 2019-02-22T11:28:15
**/
#include
#include
void data(double* x, double* y, int n); //x-横坐标,y-纵坐标,f-插值系数,n插值节点个数
void newton(double* x, double* y, double* f, int n);
void printnew(double* x, double* y, double* f, int n);
void newvalue(double* x, double* y, double* f, int n);
int main(void)
{
int n;
double *x, *y, *f;
printf("输入要插值节点的个数:");
scanf("%d", &n);
x = (double*)malloc(sizeof(double) * n);
y = (double*)malloc(sizeof(double) * n);
f = (double*)malloc(sizeof(double) * (n - 1) * n / 2);
data(x, y, n);
newton(x, y, f, n - 1);
printnew(x, y, f, n);
do {
newvalue(x, y, f, n);
} while (1);
return 0;
}
void data(double* x, double* y, int n)
{ //读取初始数据
int i = 0;
while (i < n) {
printf("x[%d]:", i);
scanf("%lf", &x[i]);
printf("y[%d]:", i);
scanf("%lf", &y[i]);
i++;
}
}
void newton(double* x, double* y, double* f, int n)
{ //建立牛顿插值多项式的系数
int i = 0, j, k = 0;
for (i = 0; i < n; i++)
for (j = 0; j < n - i; j++) {
if (i == 0)
f[k++] = (y[j + 1] - y[j]) / (x[j + 1] - x[j]);
else {
f[k] = (f[k + i - n ] - f[k + i - n - 1]) / (x[j + i + 1] - x[j]);
k++;
}
}
}
void printnew(double* x, double* y, double* f, int n)
{ //输出差商表
int i, j, k = 0;
printf("差商表:\n");
printf("x\t ");
for (i = 0; i < n; i++)
printf("f(x%d)\t\t", i);
printf("\n");
for (i = 0; i < n; i++)
printf("----------------");
printf("\n");
for (i = 0; i < n; i++) {
printf("%-10g %-10g", x[i], y[i]);
k = i - 1;
for (j = 0; j < i; j++) {
printf(" %-10g", f[k]);
k += n - 2 - j;
}
if (j == i)
printf("\n");
}
}
void newvalue(double* x, double* y, double* f, int n)
{ //根据牛顿插值多项式预测下一个节点的值
double a, *b;
int i, k = 0;
b = (double*)malloc(sizeof(double) * n);
printf("输入要要插入节点的X的值:");
scanf("%lf", &a);
b[0] = 1.0;
for (i = 0; i < n - 1; i++)
b[i + 1] = b[i] * (a - x[i]);
for (i = 0; i < n; i++) {
if (i == 0)
a = y[0];
else {
a += b[i] * f[k];
k += n - i;
}
}
printf("插值节点对应的Y的值:%g\n", a);
}
运行结果