用高斯消去法解线性方程组C++程序及结果

1、用高斯消去法解线性方程组。设有n元线性方程组如下：算法：对于k从0开始到n-2结束，进行以下步骤：首先，第k行第k列的数不能为0，若为0，则与下面不为0的行交换。将k行所有数除以第k行第k列的数.其次，进行消去：aij=aij-aik*akj,j,i=k+1,k+2,，n-1bi=bi-aik*bk,i=k+1,k+2,n-1最后，回代过程xn-1=bn-1/an-1n-1xi=bi-aijxj,I=n-2,1,0定义一个矩阵类Matrix作为基类，然后由矩阵类派生出线性方程组类Linequ。程序清单：#include<iostream>#include<cmath>u

2、sing namespace std;class Matrix /定义矩阵类public:Matrix(int dims=2) /构造函数index=dims; /保护数据赋值MatrixA=new doubleindex*index; /动态内存分配Matrix()delete MatrixA; /内存释放void setMatrix(double *rmatr) /设置矩阵值for(int i=0;i<index*index;i+)*(MatrixA+i)=rmatri; /矩阵成员赋初值 void printM(); /显示矩阵 protected: int index; doub

3、le* MatrixA; ;class Linequ:public Matrix /线性方程组类 public: Linequ(int dims=2):Matrix(dims) sums=new doubledims; solu=new doubledims; Linequ(); void setLinequ(double*a,double*b); void printL(); int Solve(); void showX(); private: double *sums; double *solu; ;void Matrix:printM() /显示矩阵的元素 cout<<&q

4、uot;The Matrix is:"<<endl; for(int i=0;i<index;i+) for(int j=0;j<index;j+) cout<<*(MatrixA+i*index+j)<<" " cout<<endl; Linequ:Linequ() deletesums; deletesolu; void Linequ:setLinequ(double *a,double *b) setMatrix(a); for(int i=0;i<index;i+) sumsi=bi;/方程

5、赋值 /显示方程 /高斯消元法求解 /输出方程的解 /方程赋值void Linequ:printL() /显示方程 cout<<"The Line eqution is:"<<endl;for(int i=0;i<index;i+)for(int j=0;j<index;j+)cout<<*(MatrixA+i*index+j)<<" " cout<<" "<<sumsi<<endl;void Linequ:showX() cout<

6、<"The Result is:"<<endl;for(int i=0;i<index;i+)cout<<"X"<<i<<"="<<solui<<endl; int Linequ:Solve() int l,k,i,j,is,p,q,m=0;double d,t;l=1;for(k=0;k<=index-2;k+) d=0.0;for(i=k;i<=index-1;i+)for(j=k;j<=index-1;j+)t=fabs(Mat

7、rixAi*index+j); if(t>d)d=t;is=i;if(d+1.0=1.0)l=0;if(l=0)cout<<"fail"<<endl;return(0);d=MatrixAk*index+k;if(d=0)m+; /输出方程的解 /解线性方程组 /消去过程d=MatrixA(k+m)*index+k; is=k+m; if(is!=k) for(j=k;j<=index-1;j+) p=k*index+j;q=is*index+j; t=MatrixAp;MatrixAp=MatrixAq;MatrixAq=t; t=su

8、msk;sumsk=sumsis;sumsis=t; d=MatrixAk*index+k;for(j=k;j<=index-1;j+) p=k*index+j;MatrixAp=MatrixAp/d;sumsk=sumsk/d;for(i=k+1;i<=index-1;i+)for(j=k+1;j<=index-1;j+)p=i*index+j;MatrixAp=MatrixAp-MatrixAi*index+k*MatrixAk*index+j; sumsi=sumsi-MatrixAi*index+k*sumsk;d=MatrixA(index-1)*index+ind

9、ex-1;if(fabs(d)+1.0=1.0)cout<<"fail"<<endl;return(0);soluindex-1=sumsindex-1/d; /回代过程 for(i=index-2;i>=0;i-)t=0.0;for(j=i+1;j<=index-1;j+)t=t+MatrixAi*index+j*soluj;solui=sumsi-t;int main() /主函数 double a=2,-0.5,-0.5,0, -0.5,2,0,-0.5, -0.5,0,2,-0.5, 0,-0.5,-0.5,2; double b4=0,