jacobi.cpp

数值分析算法jacobi方法

#include<iostream.h>
#include<stdlib.h>
#include<math.h>
void main(){
	cout<<"============================"<<endl;
	cout<<"雅可比迭代法解方程组"<<endl;
	cout<<"  x1+2*x2-2*x3=7"<<endl;
	cout<<"  x1+  x2+  x3=2"<<endl;
	cout<<"2*x1+2*x2+  x3=5"<<endl;
	cout<<"准确解：x1=1,x2=2,x3=-1"<<endl;
	cout<<"=========================="<<endl;

	int i,j,n,N,k;
	double a[10][10],b[10],x0[3],c[3],x[3];
	//............................................
	//double a[3][3]={{1,2,-2},{1,1,1},{2,2,1}};
	//double b[3]={7,2,5};
	//.............................................
	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;
	k=0;
	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];
	}	
	for(i=0;i<n;i++){c[i]=fabs(x[i]-x0[i]);}
	for(i=0;i<n;i++){
		double max=0;
		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];}
	}	

}
}