col_p.rar_列主元消元法_列主消元法_线性方程_线性方程组

#include<iostream.h> #include<math.h> void col_expunction(int n,double** a,double* b) //列主消元法函数 { double* x=new double[n]; int* q=new int [n]; for(int i=0;i<n;i++) q[i]=i; if(n==1)x[0]=b[0]/a[0][0]; //当n=1时的处理 for(int k=0;k<n-1;k++){ //选最大系数列 double max=fabs(a[q[k]][k]); int p=q[k]; for(int j=k+1;j<n;j++){ if(max<fabs(a[q[j]][k])){ max=a[q[j]][k]; p=q[j]; } } for(i=k+1;i<n;i++){ if(q[i]==p){ q[i]=q[k]; q[k]=p; break; } } for(i=k+1;i<n;i++){ //方程求解过程 double l=(a[q[i]][k])/a[p][k]; for(j=k+1;j<n;j++) a[q[i]][j]=a[q[i]][j]-l*(a[p][j]); b[q[i]]=b[q[i]]-l*b[p]; } x[n-1]=b[q[n-1]]/a[q[n-1]][n-1]; for(i=n-2;i>=0;i--){ double y=0; for(j=i+1;j<n;j++) y+=a[q[i]][j]*x[j]; x[i]=(b[q[i]]-y)/a[q[i]][i]; } } for(i=0;i<n;i++) b[i]=x[i]; } void main() { char ch; do{ int n; cout<<"Input n:"; cin>>n; double** a=new double* [n]; for(int i=0;i<n;i++) a[i]=new double[n]; double* b=new double [n]; cout<<endl<<"自动生成Hilbert矩阵?(y=yes||anykey=no):"; cin>>ch; if(ch!='y'&&ch!='Y'){ cout<<"\nInput a[i][j](1<=i,j<=n):\n"; for(i=0;i<n;i++) for(int j=0;j<n;j++) cin>>a[i][j]; cout<<"\nInput b[i](1<=i<=n):\n"; for(i=0;i<n;i++) cin>>b[i]; } else{ for(i=0;i<n;i++) for(int j=0;j<n;j++) a[i][j]=(double)1/(i+j+1); for(i=0;i<n;i++){ b[i]=0; for(int j=0;j<n;j++) b[i]+=(double)(j+1)/(i+j+1); } } col_expunction(n,a,b); cout<<endl<<"方程组的解为:"<<endl; for(i=0;i<n;i++) cout<<"x["<<i<<"]="<<b[i]<<"\t"; cout<<endl; cout<<endl<<"Continue?(y=yes||anykey=no):"; cin>>ch; cout<<endl; }while(ch=='y'||ch=='Y'); }