浙江工业大学数值计算方法实验2

实验报告一、实验目的用下列方法解线性方程1.1348 3.8326 1.16513.4017产1]9.5342'0.5301 1.7875 2.53301.5435X26.39413.41294.9317 8.76431.3142兀318.4231L1.23714.9998 10.67210.0147J民4」L16.9237J并比较计算结果精度⑴顺序消元法（2）列主元消元法二、实验方法（要求用自己的语言描述算法）•顺序消元法本代码中是将题中矩阵转化为上三角矩阵，具体流程如下：通过双重for循环【外层for循环控制作为基准的行数，内层循环计算与基准行的倍数，并且进行行相减操作（行相减的for循环不考虑在内）】，最后通过回代求解出所有的解。•列主元消元法本代码中在将矩阵转化为上三角矩阵的同时，事先需进行，预处理操作如下（化为上三角矩阵过程同顺序消元法）:在每次操作时先找出列中绝对值最大的元素，并与基准行先进行交换。三、实验代码#include<iostream>#include<iomanip>#include<fstreaa>usingnamespacestd;voiddisplay(double**a,double*b,intN);intmainO{//ifstreancinC"input・txt");//ofstreancoutoutputintN; 〃方程的阶doublemax,p;inti,j,k,1;cout«"请输入方程的阶(输入0退fli):while(cin»N&&N){double**a=newdouble*[N],*b=newdouble[N];double**c=newdouble*[N],*d=newdouble[N];double**n=newdouble*[N],*x=newdouble[N];for(i=0;i<N;i卄){a[i]=newdouble[N];c[i]=newdouble[N];jn[i]=newdouble[N];}cout«"请输入数组A：endl;for(i=0;i<N:i卄)for(j=0;j<N;j++){cin»a[i][j];c[i][j]=a[i][j];}cout«"请输入数组B：endl;for(i=0;i<N;i卄){cin»b[i];d[i]=b[i];}〃消元计算，将方程组约化为三角形方程组for(k=0;k<=N;k++)for(i=k+1;i<N;i++){m[i][k]=a[i][k]/a[k][kJ;cout«Bi[i][k]«endl;for(j=k;j<N;j++)a[i][j]-=ni[i][k]*a[k][j];

b[i]一二>[i][k]*b[kl;display(a,b,N);〃回代求解doublet=0.0;x[N-1]=b[N-1]/a[N-1][N-1];for(i=N-2;i>=0;i—){x[i]=b[i];for(j=i+l;j<N;j++)x[i]一二a[i][j]*x[j];x[i]/=a[i][i];}〃输出方程组的解cout«"方程的解为："《endl;for(i=0;i<N:i++)cout i+1<]="<〈x[i]«endl;cout«cout«endl// 分割线•cout«cout«endl;for(k=0;k<N-1;k++){max=c[k][k];for(i=k+1;i<N;i++) //for(i=k+1;i<N;i++) //选取主元if(fabs(c[i][k])>fabs(max)){max=c[i][k];1=i；}if(fabs(max)*100000<1)cout«^detA=0*«endl;else{if(11=k){ //交换行p=d[l];d[l]=d[k];d[k]=p;for(j=0;j<N;j++){p=c[l][j]；c[l][j]=c[k][j];c[k][j]=p;}display(c,d,N);}for(i=k+1;i<N;i卄){ //消元，化为三角方程组=c[i][k]/c[k][kJ;for(j=k;j<N:j++)c[i][j]-=m[i][k]*c[k][j];

d[i]-=m[i][k]*d[k];}display(c,d,N);}}if(fabs(c[N-1][N-1])*100000<1)cout«^detA=0<z«endl;else{〃回代求解x[N-1]=d[N-1]/c[N-1][N-1];for(i=N-2;i>=0;i—){x[i]=d[i];for(j=i+l;j<N;j++)x[i]-=c[i][j]*x[j];x[i]/=c[i][i];}}〃输出方程组的解cout«"方程的解依次为"<<endl;for(i=0;i<N;i++)cout i+1<〈"]="<〈x[i]«endl;free(a);free(b);free(c);free(d);free(m);free(x);}}voiddisplay(double**a,double*b,intN){for(inti=0;i<N;i++){for(intj=0;j<N;j++)cout«set曹(15)«a[i][j];cout«setw(5)<C|^«b[i]«endl;}cout«endl;

四、实验结果及其讨论本题中输入部分同过文件流读入，实验结果见图1与图2oC:\WINDOWS\system32\cmd.exe「o1「回心10・4671311.13483.83261.16513.4017!9.53420-0.00282541.98875-0.045538?!1・940383.41294.93178.76431.3142!18・42311.23714.999810.67210・0147!16.92373.0074913483.83261.16S13.4R17!9.53420-0.00282541.98875-0.045538?!1・940380-6.594815.26027-8.91638!-10.25091.23714.999810.67210・0147!16.92371.R9R151.13483.83261.16513.4017!9.53420-0.00282541.98875-0.045538?!1・940380-6.594815.26027-8.91638!-10.2509-2.22045e-160.8216999.4019?-3.69366!6.530012334.121.13483.83261.16513.4017!9.53420-0.00282541.98875-0.045538?!1・9403800-4636.7197.3764!-4539.33一2・2204£&一160.8216999.4R197一？.69266!6.52001-290.8261.13483.83261.16513.4017!9.53420-0.00282541.98875-0.045538?!1・9403800一4636・亢97.3764!-4539.33-2.22045e-16-1.11022e-1658?・？81-16.9375!570.843-0.1267671.13483.83261.16513.4017!9.53420一0・00282541.98875一Q・0455387!丄・9403800-4636.7197.3764!-4539.33-2.22045e-16-1.11022e-16-1.1368?e-13-4.5934!-4.5934方程的解为:x[2]=lx[3]=lx[4]=l图1C:\WINDOWS\system32\cmd.exe |且||旦||旦|3.41294.93178.76431.3142!18・42310.53011・78752.5331.5435!6.39411.13483・83261.16513・401719.53421.23714.999810.67210・0147!16.92373.41294.93178.76431.3142!18・423101.02151.171711.33938!3.5325802.19279-1.749062.96472!3.4084603.212177.49524-0.461668!10・24573.41294.93178.76431.3142!18・423103.212177.49524-0.461668!10・245702.19279-1.749062.96472!3.4084600215丄・171711.33938!3.532583.41294.93178.76431.3142!18・423103.212177.49524-0.461668!10・245700-6.86573.27988!-3.5858100-1.211841.48619!0・274353.41294.93178.76431.3142!18・423103.212177.49524-0.461668!10・245700-6.86573.27988!-3.5858100