我有这个方程式


然后从中找到多项式

我正在尝试像这样实现它:

for (int n=0;n<order;n++){
    df[n][0]=y[n];
    for (int i=0;i<N;i++){ //N number of points

        df[n][i]+=factorial(n,i)*y[i+n-1];
    }

    }

for (int i=0;i<N;i++){

    term=factorial(s,i);
    result*=df[0][i]*term;
    sum+=result;
    }

return sum;

1)我不确定如何在函数中实现每个参数的符号,如您所见,它变为'positive','negative','positive'...

2)我不确定是否有任何错误...

谢谢!

- - - - - - - - - - - 阶乘 - - - - - - - - - - - - - - -
int fact(int n){
//3!=1*2*3
if (n==0) return 1;
else
return n*fact(n-1);

}

double factorial(double s,int n){
//(s 3)=s*(s-1)*(s-2)/6
if ((n==0) &&(s==0)) return 1;
else
    return fact(s)/fact(n);


}

最佳答案

好吧,我知道您想使用具有等距点的牛顿插值多项式(更具体地说是牛顿-格雷戈里正向差分插值多项式)来近似计算给定x = X的值f(x)。
假设s =(X-x0)/ h,其中x0是第一个x,而h是获得x其余部分的步骤,而您知道f的确切值:
认为:

double coef (double s, int k)
{
    double c(1);
    for (int i=1; i<=k ; ++i)
        c *= (s-i+1)/i ;
    return c;
}

double P_interp_value(double s, int Num_of_intervals , double f[] /* values of f in these points */)    // P_n_s
{

    int N=Num_of_intervals ;

    double *df0= new double[N+1]; // calculing df only for point 0

    for (int n=0 ; n<=N ; ++n)  // n here is the order
    {
        df0[n]=0;
        for (int k=0, sig=-1; k<=n; ++k, sig=-sig) // k here is the "x point"
        {
            df0[n] += sig * coef(n,k) * f[n-k];
        }
    }

    double P_n_s = 0;

    for (int k=0; k<=N ; ++k )   // here k is the order
    {
        P_n_s += coef(s,k)* df0[k];
    }
    delete []df0;

    return P_n_s;
}


int main()
{
    double s=0.415, f[]={0.0 , 1.0986 , 1.6094 , 1.9459 , 2.1972 };

    int n=1; // Num of interval to use during aproximacion. Max = 4 in these example
    while (true)
    {
    std::cin >> n;
    std::cout << std::endl << "P(n=" << n <<", s=" << s << ")= " << P_interp_value(s, n, f)  << std::endl ;
    }
}

它打印:

1个

P(n = 1,s = 0.415)= 0.455919

2

P(n = 2,s = 0.415)= 0.527271

3

P(n = 3,s = 0.415)= 0.55379

4

P(n = 4,s = 0.415)= 0.567235

与之比较:
http://ecourses.vtu.ac.in/nptel/courses/Webcourse-contents/IIT-KANPUR/Numerical%20Analysis/numerical-analysis/Rathish-kumar/rathish-oct31/fratnode8.html

有用。现在我们可以开始优化这些代码。

10-06 05:22