【C/C++】實現牛頓迭代

 1 #include<bits/stdc++.h> 
 2 using namespace std;  3 
 4 
 5 /*(x+2)^2 +1  6  -2(x-1)^2+7  7 
 8 */
 9 double f(double x){  10     return 4-x- pow(2,x);  11 }  12 double df(double x){  13     return -1 - pow(2,x)*log(2);  14 }  15 
 16 //二分法
 17 void binary_search(double l,double r,double e){  18     
 19     double mid = (l+r)/2;  20     int manN = 1000;  21     int k = 1;  22     int flag  = 0;  23     while(1){  24         mid = (l+r)/2;  25         if(fabs(f(mid)) < e){  26             flag = 1;  27             break;  28  }  29         if(k>=manN){  30             flag = 0;  31             break;  32  }  33         if(f(l)*f(mid)<0){  34             r = mid;  35         }else if(f(mid)*f(r)<0){  36             l = mid;  37  }  38         k++;  39  }  40     if(flag){  41         printf("二分次數是：%d,解爲：%.8lf\n",k,mid);  42  }  43 }  44  
 45 void NewTon(double x0,double e,int N){  46     //牛頓法求根，起始點x0開始  47     //N是最大迭代次數
 48     int flag = 0;  //1是奇異 2是找到了 3是失敗 
 49     double x1,result;  50     int k = 1;  51     while(1){  52         if(df(x0) == 0){  53             flag = 1;  54             break;  55  }  56         x1 = x0 - f(x0)/df(x0);  57         if(fabs(x1-x0) < e){  58             result = x1;  59             flag = 2;  60             break;  61  }  62         if(k == N){  63             flag = 3;  64             break;  65  }  66         k++;  67         //printf("%lf\n",x0);
 68         x0 = x1;  69         
 70  }  71     if(flag == 2){  72         printf("找到了，而且迭代次數是：%d，根爲：%.8lf\n",k,result);  73     }else if(flag == 1){  74         printf("函數不可導");  75     }else if(flag == 3){  76         printf("超出局部收斂範圍，迭代失敗！\n");  77     }else{  78         printf("return!");  79  }  80     return;  81 }  82 int main(){  83     
 84 // double x0;  85 // double e;  86 // int N = 100;  87 //    //while(1){  88 // printf("輸入起始點、精度、最大迭代次數：");  89 // cin>>x0>>e>>N;  90 // NewTon(x0,e,N);  91 //    
 92 //
 93 // printf("-------------\n");  94 // printf("請輸入二分法左右區間、精度：");  95 // double l,r,e1;  96 // cin>>l>>r>>e1;  97 // binary_search(l,r,e1);
 98     double x = 1.38616943;  99     printf("%.10lf",f(x)); 100     
101 }