【C/C++】实现牛顿迭代 

  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("二分次数是：%d,解为：%.8lf\n",k,mid);
 42     }
 43 }
 44  
 45 void NewTon(double x0,double e,int N){
 46     //牛顿法求根，起始点x0开始
 47     //N是最大迭代次数
 48     int flag = 0;  //1是奇异 2是找到了 3是失败 
 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，并且迭代次数是：%d，根为：%.8lf\n",k,result);
 73     }else if(flag == 1){
 74         printf("函数不可导");
 75     }else if(flag == 3){
 76         printf("超出局部收敛范围，迭代失败！\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("输入起始点、精度、最大迭代次数：");
 89 //        cin>>x0>>e>>N;
 90 //        NewTon(x0,e,N);        
 91 //    
 92 //
 93 //    printf("-------------\n");
 94 //    printf("请输入二分法左右区间、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 }

 

posted @ 2018-05-31 20:55  pigcv  阅读(1331)  评论(0)  编辑  收藏  举报