guase_seidel迭代.cpp

数值分析算法Guase_Seidel迭代

#include<iostream.h>
#include<stdlib.h>
#include<math.h>
void main(){
	cout<<"============================"<<endl;
	cout<<"Gause-Seidel迭代法解方程组"<<endl;
	cout<<"    x1+0.9*x2+0.9*x3=1.9"<<endl;
	cout<<"0.9*x1+    x2+0.9*x3=2.0"<<endl;
	cout<<"0.9*x1+0.9*x2+	 x3=1.7"<<endl;
	cout<<"准确解：x1=1,x2=2,x3=-1"<<endl;
	cout<<"=========================="<<endl;

	int i,j,n,N,k;
	double x0[3],c[3],x[3],f[3];
	//............................................a[10][10],b[10],
	double a[3][3]={{1,0.9,0.9},{0.9,1,0.9},{0.9,0.9,1}};
	double b[3]={1.9,2.0,1.7};
	//.............................................
	double e,T;
	cout<<"输入维数n:";
	cin>>n;
	/*cout<<"输入矩阵A:"<<endl;
	for(i=0;i<n;i++)
		for(j=0;j<n;j++){
			cout<<"a["<<i<<"]["<<j<<"]=";
			cin>>a[i][j];
		}
	cout<<"输入右端项b:"<<endl;
	for(i=0;i<n;i++){
		cout<<"b["<<i<<"]=";
		cin>>b[i];
	}*/
	cout<<"输入初始迭代向量x0:"<<endl;
	for(i=0;i<n;i++){
		cout<<"x0["<<i<<"]=";
		cin>>x0[i];
	}
	cout<<"输入允许的误差e=";
	cin>>e;
	cout<<"输入允许的最大迭代次数N:";
	cin>>N;
///////////////////////////////////
  while(N--){
	for(i=0;i<n;i++){
		T=0;
		for(j=0;j<n;j++){
			if(j!=i)T=T+a[i][j]*x0[j];
		}
		x[i]=(b[i]-T)/a[i][i];
		f[i]=x0[i];
		x0[i]=x[i];
		}	
	for(i=0;i<n;i++){c[i]=fabs(f[i]-x0[i]);}	
	double max=0;
	for(i=0;i<n;i++){
		max=max+c[i];
	if(max<e){
		cout<<"jacobi求解得:"<<endl;
		for(i=0;i<n;i++){
			cout<<"x["<<i<<"]="<<x[i]<<endl;
		}
		exit(1);
	}
	}
  }
}
















	/*
	//k=0;
//	while(N--){
		
	for(j=1;j<n;j++){T=0;
		T=T+a[0][j]*x0[j];
	}
	x[0]=(b[0]-T)/a[0][0];	
	for(i=1;i<n-1;i++){
		double M=0;
		for(j=0;j<i-1;j++){
		M=M+a[i][j]*x[j];}
		double N=0;
		for(j=i+1;j<n;j++){	
		N=N+a[i][j]*x0[j];}
		x[i]=(b[i]-M-N)/a[i][i];
	}
	double L=0;
	for(j=0;j<n-1;j++){	
		L=L+a[n-1][j]*x[j];}
	x[n-1]=(b[n-1]-L)/a[n-1][n-1];	

	for(i=0;i<n;i++){
		c[i]=fabs(x[i]-x0[i]);}
	double max=0;
	for(i=0;i<n;i++){		
		max=max+c[i];
	if(max<e){
		cout<<"jacobi求解得:"<<endl;
		for(i=0;i<n;i++){
			cout<<"x["<<i<<"]="<<x[i]<<endl;
		}
		exit(1);
	}
//	else 
//		for(i=0;i<n;i++){x0[i]=x[i];}
//	}	

}
}*/