diedai.cpp

用c++编写的简单迭代发和牛顿迭代发以及埃特金加整收敛法的有效程序

#include<math.h>
#include<iostream.h>
#include<stdio.h>
#define EPS 0.00001

      
		   double f( double x)
		   {
			   double a=x*x*x;
			   double b=2*x;
			   double c=a-b-5;
			   return c;
		   }
	 		erfenfa(double a,double b, int c)//二分法
			{    
				double root,ya, yb,yroot;
			    int i; int acu_c;
			         ya=f(a);
					 cout<<ya<<endl;
					 yb=f(b);
					 cout<<yb<<endl;
					 if(ya*yb>0)
					 {
						 cout<<"不能求根，条件不满足"<<endl;
					 }
					 else{
						 
					
			      	for(i=1; i<c;i++)
						 {
							  root=(a+b)/2;  yroot=f(root);
							  		 
							  printf("root=%10.6lf\n",root); 
							  
					
							  if (yroot==0)
							  {
								  a=root; b=root;
							  }
							  else if (yb*yroot>0)
							  {
								  b=root;yb=yroot;
							  }
							  else
							  {
								  a=root; ya=yroot;
							  }
							  if(fabs(b-a)<EPS) break;
						  }
					 }
						  root=(a+b)/2; yroot=f(root);   
							
                           acu_c=i;
						     printf("%10.6lf\n",root);
						   cout<<yroot<<endl;
						   cout<<"一共迭代了"<<acu_c<<"次"<<endl;
					 
						   }
			double  g(double x)
			{
				return(pow((2.0*x+5.0),1.0/3.0));
			}
			jiandandiedai(double a, double b,  double x0, int c)//简单迭代法
			{   
			//	cout<<"ok"<<endl;
				int k=1; double x1;
			while(k<=c)
			{
				x1=g(x0);
				cout<<x1<<endl;
				if((x1<a)||(x1>b))
				{
					printf("Re-select a proper initial value x0!\n");
				}
				else
				{
					if (fabs(x1-x0)<EPS)
					{
						printf("Method succeed !\n");
						printf("root=%10.6lf\n",x1);
						break;
					}
						x0=x1; 
						k++;
					
				}
			}
			printf("diedai times=%d\n",k);
			if(k>c) printf("Method failed!\n");
			}
			void aitejin(double a, double b,double x0, int c)//aige jin 
			{   		cout<<"ok"<<endl;
				int k=1;
			     double x1, x2, x3;
				 while (k<=c)
				 {
					 x1=g(x0);
					 x2=g(x1);
					 x3=((x0*x2-x1*x1)/(x0-2*x1+x2));
					
					 cout<<x3<<endl;
					 if((x3<a)||(x3>b))
					 {
						 	printf("Re-select a proper initial value x0!\n");
					 }
					 else
					 {
						 if(fabs(x3-x0)<EPS)
						 {
							 printf("Method succeed !\n");
						printf("root=%10.6lf\n",x1);
						break;
						 }
						 x0=x3;
						 k++;
					 }
				 }
            printf("diedai times=%d\n",k);
				 if(k>c) printf("Method failed!\n");
			 }



   
             double daoshu(double x)
			 {
				 return (3*x*x-2);
			 }
			 void newton(double a,double b, double x0,int c)//牛顿迭代法
			 {
				 int k=1; double x;
				 while(k<c)
				 {   
					 x=x0-f(x0)/daoshu(x0);
					 cout<<x<<endl;
					 if((x<a)||(x>b))
					 {
					printf("Re-select a proper initial value x0!\n");
					 }
					 else
					 { 
						 if(fabs(x-x0)<EPS)
						{
						printf("方法成功 !\n");
						printf("root=%10.6lf\n",x);
						break;
						 }
						x0=x; 
						k++;
					 }
				 }
				 printf("diedai times=%d\n",k);
				 if(k>c) printf("Method failed!\n");
			 }

					 



	void  main()
	{                  
		               double a=2.0 , b=3.0 ,  x0=(a+b)/2.0;  int c=30;
					char s='y';  int x=1; int i;
					cout<<"              "<<"请选择你所需要的求根方法"<<endl;
					while(s=='y')
					{  
					   cout<<"1:为二分法"<<endl;
                       cout<<"2:为简单迭代法"<<endl;
                       cout<<"3:为牛顿迭代法"<<endl;
                      cout<<"4:埃特金加整收敛法"<<endl;
                          cout<<endl;
                    cout<<"请选择"<<endl;
                    cout<<"请输入你选择的序号:";
                         cin>>i;
                   switch(i)
				   {  
				   case 1:
                erfenfa(a,b,c);
			   break ;
              case 2:cout<<"你选择简单迭代法"<<endl;
			
                   jiandandiedai(a,b,x0,c);
			break;
            case 3:
               	cout<<"你选择的是牛顿迭代法"<<endl;
                 newton( a, b,  2.5, c);
            	break;
             case 4:
	        cout<<"你选择的是埃特金加整收敛法"<<endl;
			cout<<"ok"<<endl;
			aitejin(a,b,x0,c);
	         break;
               case 0:
              	s='n';
	            break;
	  
				   }
if(x==1){
	cout<<"要继续吗？(y/n)";
	cin>>s;
	cout<<endl;
}
}
			 
		   }