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大连理工大学 2015年矩阵上机编程作业

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本答案说明：该1-10题所有结果均用C++完成，其中有些题目编写的代码比较长，为了使得看起来比较容易懂，程序的架构清晰，把main()函数提到了前面，如果想要调试的话，请把main()函数之后附的的各种实现函数提前，程序就能正常运行。

该11-15题需要作图，所以采用Matlab编程实现。

1.设, 其精确值为.(1)编制按从大到小的顺序, 计算的通用程序(2)编制按从小到大的顺序, 计算的通用程序(3)按两种顺序分别计算并指出有效位数（编制程序时用单精度）(4)通过本上机题，你明白了什么答案：通过分析我们发现利用编制从大到小得到的精度较高，一般先加小数再加大数，精度会发生缺失。

运行结果如下：代码如下：#include <iostream.h>//第1问void nFromMintoMax(float n){float sum;sum=0.0;for(float i=2;i<n;i++){sum=sum+ (float)1.0/(i*i-1);}cout<<"编制从大到小的计算结果"<<" "<<sum<<endl;}//第2问void nFromMaxtoMin(float n){float sum;sum=0.0;for(float i=n;i<1;i--){sum=sum+(float)1.0/(i*i-1);}cout<<"编制由小到大的计算结果"<<" "<<sum<<endl;}void main (){cout<<"S(100):"<<endl;nFromMintoMax(100); //调用第一问的函数nFromMaxtoMin(100); //调用第二问的函数cout<<"S(10000):"<<endl;nFromMintoMax(10000);nFromMaxtoMin(10000);cout<<"S(1000000):"<<endl;nFromMintoMax(1000000);nFromMaxtoMin(1000000);}2.秦九韶算法。

已知n次多项式，用秦九韶算法编写通用的程序计算函数在错误!未找到引用源。

点的值，并计算在错误!未找到引用源。

点的值.(提示：编写程序时，输入系数向量和点错误!未找到引用源。

，输出结果，多项式的次数可以通过向量的长度来判断)秦九韶算法公式为：秦九韶算法输出结果：秦九韶算法代码：#include <iostream.h>//秦九韶算法,a代表系数，n代表系数总数void QinJS(float a[],int n,float x){float sum=a[0];for(int i=0;i+1<n;i=i+1){sum=sum*x+a[i+1];}cout<<"秦九韶算法计算结果为"<<" "<<sum<<endl;}void main(){cout <<"请输入X"<<endl;float x;cin>>x;cout <<"请依次输入系数总数n和n个系数"<<endl;int n;cin>>n;float a[10];for(int i=0;i<n;i++){float j;cin>>j;a[i]=j;// cout<<a[i]<<endl;}//调用秦九韶算法QinJS(a,n,x);}3.分别用Gauss消元法和列主元消去法编程求解方程组Ax=b，其中，实验结果为：实验代码为：#include <iostream.h>#include <math.h>#include<iomanip.h>void main (){//Gauss 消元double a[9][10]={{31,-13,0,0,0,-10,0,0,0,-15},{-13,35,-9,0,-11,0,0,0,0,-27},{0,-9,31,-10,0,0,0,0,0,-23},{0,0,-10,79,-30,0,0,0,-9,0},{0,0,0,-30,57,-7,0,-5,0,-20},{0,0,0,0,-7,47,-30,0,0,12},{0,0,0,0,0,-30,41,0,0,-7},{0,0,0,0,-5,0,0,27,-2,7},{0,0,0,-9,0,0,0,-2,29,10}};Gauss(a,9,10); //高斯消元cout<<"Gauss消元的上三角矩阵为"<<endl;display(a,9,10); //显示矩阵SolveOne(a,9,10); //求解Ax=b，A为上三角矩阵//列主元消元double b[9][10]={{31,-13,0,0,0,-10,0,0,0,-15},{-13,35,-9,0,-11,0,0,0,0,-27},{0,-9,31,-10,0,0,0,0,0,-23},{0,0,-10,79,-30,0,0,0,-9,0},{0,0,0,-30,57,-7,0,-5,0,-20},{0,0,0,0,-7,47,-30,0,0,12},{0,0,0,0,0,-30,41,0,0,-7},{0,0,0,0,-5,0,0,27,-2,7},{0,0,0,-9,0,0,0,-2,29,10}};Lie(b,9,10); //列主元消元cout<<"列主元消元的上三角矩阵为"<<endl;display(b,9,10); //显示SolveOne(b,9,10); //求解Ax=b, A为上三角矩阵}//输出二维数组元素，这个函数是用来显示矩阵，用来调试void display(double a[9][10],int r_size1,int r_size2){for(int i=0; i<r_size1; i++){for(int j=0; j<r_size2; j++){cout<<setprecision(8)<<setw(12)<<a[i][j]<<"";if(j+1==r_size2){cout<<endl;}}}}//Ax=b的解答，A为上三角矩阵void SolveOne(double a[9][10],int m,int n){int j=n-2;double answer[9];for (int s=m-1;s>=0;s--){answer[j]=a[s][n-1]/a[s][j];for(int i=0;i<=s-1;i++){a[i][n-1]=a[i][n-1]-answer[j]*a[i][j];}j--;}cout<<"解答的结果为："<<endl;for(int i=0;i<9;i++){cout<<setprecision(8)<<setw(12)<<answer[i]<<" ";}cout<<endl;}//Gauss 消元解法//先转化为上三角矩阵void Gauss(double a[9][10],int m,int n){double r[9]; //r为每次的倍数int k=0;for (int nowi=0,nowj=0;nowi<m-1 && nowj<n-1;nowi++,nowj++){ // 计算要乘的倍数for(int s=nowi;s<m;s++){r[s]=a[s+1][nowj]/a[nowi][nowj];}// 每次根据每行的倍数将所有数处理一遍,变成(1,0，0，0)Tfor (int i=nowi;i<m-1;i++){for(int j=nowj;j<n;j++){a[i+1][j]=a[i+1][j]-r[i]*a[nowi][j];}}}}// 发现绝对值最大的元素所在一行和当前的一行做交换void change(double a[9][10],int m,int n,int nowi,int nowj){int record=nowi;//记录该和哪一行做交换bool flag=true; //标志是否需要做交换double max=a[nowi][nowj];for(int i=nowi+1;i<m-1;i++){if(max<fabs(a[i][nowj])){max=a[i][nowj];record=i;flag=false;}}//行与行之间交换if(flag==false){for(int j=nowj;j<n;j++){double s;s=a[nowi][j];a[nowi][j]=a[record][j];a[record][j]=s;}}}//列主元消元解法,转化为上三角矩阵void Lie(double a[9][10],int m,int n){double r[9]; //r为每次的倍数int k=0;for (int nowi=0,nowj=0;nowi<m-1 && nowj<n-1;nowi++,nowj++){//与Guass不同的时，每次要检查是否需要交换行change(a,9,10,nowi,nowj);// 计算要乘的倍数for(int s=nowi;s<m;s++){r[s]=a[s+1][nowj]/a[nowi][nowj];}// 每次根据每行的倍数将所有数处理一遍,变成(1,0，0，0)Tfor (int i=nowi;i<m-1;i++){for(int j=nowj;j<n;j++){a[i+1][j]=a[i+1][j]-r[i]*a[nowi][j];}}}}4.编程求解题3中矩阵错误!未找到引用源。

的LU分解及列主元的LU分解（求出L,U和P），并用LU分解的方法求A的逆矩阵及A的行列式运行实验结果如下图：其代码如下所示：#include <iostream.h>#include<iomanip.h>void main(){float a[9][9]={{31,-13,0,0,0,-10,0,0,0},{-13,35,-9,0,-11,0,0,0,0},{0,-9,31,-10,0,0,0,0,0},{0,0,-10,79,-30,0,0,0,-9},{0,0,0,-30,57,-7,0,-5,0},{0,0,0,0,-7,47,-30,0,0},{0,0,0,0,0,-30,41,0,0},{0,0,0,0,-5,0,0,27,-2},{0,0,0,-9,0,0,0,-2,29}};float L[9][9];LU(a,L,9,9); //LU分解cout<<"LU分解的L矩阵为"<<endl;display(L,9,9);cout<<"LU分解的U矩阵为"<<endl;display(a,9,9);cout<<endl;}//定义矩阵相乘void XMatirx(float LL[9][9],float a[9][9],int m,int n){ float c[9][9];for (int i=0;i<m;i++){for(int j=0;j<n;j++){float sum=0;for(int s=0;s<n;s++){sum=sum+LL[i][s]*a[s][j];if(i==0 && j==0 && s==0){// cout<<LL[i][s]<<" "<<a[0][0]<<endl;// cout<<LL[i][s]*a[s][j]<<endl;}}c[i][j]=sum;}}//写回到B数组中，即为最终的Ufor (int i1=0;i1<m;i1++){for(int j=0;j<n;j++){a[i1][j]=c[i1][j];}}}//输出二维数组元素，这个函数是用来显示矩阵，用来调试void display(float a[9][9],int r_size1,int r_size2){for(int i=0; i<r_size1; i++){for(int j=0; j<r_size2; j++){cout<<setprecision(3)<<setw(12)<<a[i][j]<<"";if(j+1==r_size2){cout<<endl;}}}}//LU 分解void LU(float a[9][9],float L[9][9],int m,int n){float r[9]; //r为每次的倍数int k=0;float LL[9][9];//临时矩阵专门用来存储当前的L1，L2，L3 //初始化L矩阵for(int si=0;si<m;si++){for(int sj=0;sj<n;sj++){if(si==sj){L[si][sj]=1;} else{L[si][sj]=0;}}}for (int nowi=0,nowj=0;nowi<m-1 && nowj<n-1;nowi++,nowj++){ //初始化LL矩阵for(int si=0;si<m;si++){for(int sj=0;sj<n;sj++){if(si==sj){LL[si][sj]=1;} else{LL[si][sj]=0;}}}// display(LL,9,9);// 计算要乘的倍数for(int s=nowi;s<m-1;s++){r[s]=a[s+1][nowj]/a[nowi][nowj];//填充L矩阵L[s+1][nowj]=r[s];LL[s+1][nowj]=-r[s];}//调用矩阵相乘公式XMatirx(LL,a,9,9);}}5.编制程序求解矩阵A的cholesky分解，并用程序求解方程组Ax=b，其中解答：使用上述矩阵，所得到的结果如图：其代码为：//主函数代码：#include <iostream.h>#include <math.h>#include<iomanip.h>void main(){double a[4][4]={{2,1,-1,1},{1,5,2,7},{-1,2,10,1},{1,7,1,11}};double answer[4]={13,-9,6,0};double L[4][4]; //L 矩阵double LT[4][4]; // LT矩阵InitL(L,4,4);//初始化L矩阵Choskey(a,L,4,4); //进行Choskey分解display(L,LT,4,4);//显示L 和LT//L*y=b, LT*x=ySolveOne(L,answer,4,4); // 先利用上三角矩阵求解ySolveTwo(LT,answer,4,4); // 利用下三角矩阵求解x}//Choskey分解，分解成L和LTvoid Choskey(double a[4][4],double L[4][4],int m,int n){for(int j=0;j<n;j++){for(int i=j;i<m;i++){if(i==j){double sum=0;for(int k=0;k<j;k++){sum=sum+L[j][k]*L[j][k];}L[i][j]=sqrt(a[i][j]-sum);}else{double sum=0;for(int k=0;k<j;k++){sum=sum+L[i][k]*L[j][k];}L[i][j]=(a[i][j]-sum)/L[j][j];}}}}// 初始化L矩阵void InitL(double L[4][4],int m,int n){for(int i=0;i<m;i++){for(int j=0;j<n;j++){if(i<j){L[i][j]=0;}}}}//显示L和LT矩阵void display(double L[4][4],double LT[4][4],int m,int n){cout<<"Choskey分解的L矩阵为："<<endl;for(int Li=0;Li<m;Li++){for(int j=0;j<n;j++){cout<<setprecision(8)<<setw(12)<<L[Li][j]<<"";}cout<<endl;}cout<<"Choskey分解的LT矩阵为："<<endl;for(int i=0;i<m;i++){for(int j=0;j<n;j++){cout<<setprecision(8)<<setw(12)<<L[j][i]<<"";LT[i][j]=L[j][i];}cout<<endl;}}//Ax=b的解答，A为上三角矩阵void SolveTwo(double LT[4][4],double answer[4],int m,int n){ int j=n-1;for (int s=m-1;s>=0;s--){answer[j]=answer[j]/LT[s][j];for(int i=s-1;i>=0;i--){answer[i]=answer[i]-answer[j]*LT[i][j];}j--;}cout<<"解答的最终结果X为："<<endl;for(int i=0;i<4;i++){cout<<setprecision(8)<<setw(12)<<answer[i]<<" ";}cout<<endl;}//Ax=b的解答，A为下三角矩阵void SolveOne(double L[4][4],double answer[4],int m,int n){int j=0;for (int s=j;s<m;s++){answer[j]=answer[j]/L[s][j];for(int i=j+1;i<m;i++){answer[i]=answer[i]-answer[j]*L[i][j];}j++;}cout<<"解答的中间结果Y为："<<endl;for(int i=0;i<4;i++){cout<<setprecision(8)<<setw(12)<<answer[i]<<" ";}cout<<endl;}6.用追赶法编制程序求解方程组Ax=b，其中，追赶法的核心就是Ax=b，→LUx=b→Ly=bUx=y所以思路为：首先进行LU分解，然后利用上述所示公式进行求解，可以看到，该题只不过是结合了第三题和第五题：实验结果如图所示：实验的代码为：因为本题主要是把LU分解和第五题的分两步解答结合起来，所以只给出了主函数，里面的各种调用函数，都可以在第三题和第五题的代码中找到，只需要改变一下二维数组的大小即可，所以不再详述。

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大连理工大学概率上机作业

大连理工大学概率上机作业

大连理工大学概率上机作业第一次上机作业1.利用Matlab自带命令产生1000个均匀随机变量服从U(0,1)。

>> unifrnd(0,1,20,50)ans =Columns 1 through 100.8147 0.6557 0.4387 0.7513 0.3517 0.1622 0.1067 0.8530 0.7803 0.54700.9058 0.0357 0.3816 0.2551 0.8308 0.7943 0.9619 0.6221 0.3897 0.29630.1270 0.8491 0.7655 0.5060 0.5853 0.3112 0.0046 0.3510 0.2417 0.74470.9134 0.9340 0.7952 0.6991 0.5497 0.5285 0.7749 0.5132 0.4039 0.18900.6324 0.6787 0.1869 0.8909 0.9172 0.1656 0.8173 0.4018 0.0965 0.68680.0975 0.7577 0.4898 0.9593 0.2858 0.6020 0.8687 0.0760 0.1320 0.18350.2785 0.7431 0.4456 0.5472 0.7572 0.2630 0.0844 0.2399 0.9421 0.36850.5469 0.3922 0.6463 0.1386 0.7537 0.6541 0.3998 0.1233 0.9561 0.62560.9575 0.6555 0.7094 0.1493 0.3804 0.6892 0.2599 0.1839 0.5752 0.78020.9649 0.1712 0.7547 0.2575 0.5678 0.7482 0.8001 0.2400 0.0598 0.08110.1576 0.7060 0.2760 0.8407 0.0759 0.4505 0.4314 0.4173 0.2348 0.92940.9706 0.0318 0.6797 0.2543 0.0540 0.0838 0.9106 0.0497 0.3532 0.77570.9572 0.2769 0.6551 0.8143 0.5308 0.2290 0.1818 0.9027 0.8212 0.48680.4854 0.0462 0.1626 0.2435 0.7792 0.9133 0.2638 0.9448 0.0154 0.43590.8003 0.0971 0.1190 0.9293 0.9340 0.1524 0.1455 0.4909 0.0430 0.44680.1419 0.8235 0.4984 0.3500 0.1299 0.8258 0.1361 0.4893 0.1690 0.30630.4218 0.6948 0.9597 0.1966 0.5688 0.5383 0.8693 0.3377 0.6491 0.50850.9157 0.3171 0.3404 0.2511 0.4694 0.9961 0.5797 0.9001 0.7317 0.51080.7922 0.9502 0.5853 0.6160 0.0119 0.0782 0.5499 0.3692 0.6477 0.81760.9595 0.0344 0.2238 0.4733 0.3371 0.4427 0.1450 0.1112 0.4509 0.7948Columns 11 through 200.6443 0.3111 0.0855 0.0377 0.0305 0.0596 0.1734 0.9516 0.0326 0.25180.3786 0.9234 0.2625 0.8852 0.7441 0.6820 0.3909 0.9203 0.5612 0.29040.8116 0.4302 0.8010 0.9133 0.5000 0.0424 0.8314 0.0527 0.8819 0.61710.5328 0.1848 0.0292 0.7962 0.4799 0.0714 0.8034 0.7379 0.6692 0.26530.3507 0.9049 0.9289 0.0987 0.9047 0.5216 0.0605 0.2691 0.1904 0.82440.9390 0.9797 0.7303 0.2619 0.6099 0.0967 0.3993 0.42280.3689 0.98270.8759 0.4389 0.4886 0.3354 0.6177 0.8181 0.5269 0.5479 0.4607 0.73020.5502 0.1111 0.5785 0.6797 0.8594 0.8175 0.4168 0.9427 0.9816 0.3439 0.6225 0.2581 0.2373 0.1366 0.8055 0.7224 0.6569 0.4177 0.1564 0.5841 0.5870 0.4087 0.4588 0.7212 0.5767 0.1499 0.6280 0.9831 0.8555 0.1078 0.2077 0.5949 0.9631 0.1068 0.1829 0.6596 0.2920 0.3015 0.6448 0.9063 0.3012 0.2622 0.5468 0.6538 0.2399 0.5186 0.4317 0.7011 0.3763 0.8797 0.4709 0.6028 0.5211 0.4942 0.8865 0.9730 0.0155 0.6663 0.1909 0.8178 0.2305 0.7112 0.2316 0.7791 0.0287 0.6490 0.9841 0.5391 0.4283 0.2607 0.8443 0.2217 0.4889 0.7150 0.4899 0.8003 0.1672 0.6981 0.4820 0.5944 0.1948 0.1174 0.6241 0.9037 0.1679 0.4538 0.1062 0.6665 0.1206 0.0225 0.2259 0.2967 0.6791 0.8909 0.9787 0.4324 0.3724 0.1781 0.5895 0.4253 0.1707 0.3188 0.3955 0.3342 0.7127 0.8253 0.1981 0.1280 0.2262 0.3127 0.2277 0.4242 0.3674 0.6987 0.5005 0.0835 0.4897 0.9991 0.3846 0.1615 0.4357 0.5079 0.9880 0.1978 0.4711 0.1332 0.3395 0.1711 0.5830 0.1788Columns 21 through 300.4229 0.7788 0.2548 0.1759 0.6476 0.5822 0.4046 0.3477 0.8217 0.5144 0.0942 0.4235 0.2240 0.7218 0.6790 0.5407 0.4484 0.1500 0.4299 0.8843 0.5985 0.0908 0.6678 0.4735 0.6358 0.8699 0.3658 0.5861 0.8878 0.5880 0.4709 0.2665 0.8444 0.1527 0.9452 0.2648 0.7635 0.2621 0.3912 0.1548 0.6959 0.1537 0.3445 0.3411 0.2089 0.3181 0.6279 0.0445 0.7691 0.1999 0.6999 0.2810 0.7805 0.6074 0.7093 0.1192 0.7720 0.7549 0.3968 0.4070 0.6385 0.4401 0.6753 0.1917 0.2362 0.9398 0.9329 0.2428 0.8085 0.7487 0.0336 0.5271 0.0067 0.7384 0.1194 0.6456 0.9727 0.4424 0.7551 0.8256 0.0688 0.4574 0.6022 0.2428 0.6073 0.4795 0.1920 0.6878 0.3774 0.7900 0.3196 0.8754 0.3868 0.9174 0.4501 0.6393 0.1389 0.35920.2160 0.3185 0.5309 0.5181 0.9160 0.2691 0.4587 0.5447 0.6963 0.7363 0.7904 0.5341 0.6544 0.9436 0.0012 0.7655 0.6619 0.6473 0.0938 0.3947 0.9493 0.0900 0.4076 0.6377 0.4624 0.1887 0.7703 0.5439 0.5254 0.6834 0.3276 0.1117 0.8200 0.9577 0.4243 0.2875 0.3502 0.7210 0.5303 0.7040 0.6713 0.1363 0.7184 0.2407 0.4609 0.0911 0.6620 0.5225 0.8611 0.4423 0.4386 0.6787 0.9686 0.6761 0.7702 0.5762 0.4162 0.9937 0.4849 0.0196 0.8335 0.4952 0.5313 0.2891 0.3225 0.6834 0.8419 0.2187 0.3935 0.3309 0.7689 0.1897 0.3251 0.6718 0.7847 0.5466 0.8329 0.1058 0.6714 0.4243 0.1673 0.4950 0.1056 0.6951 0.4714 0.4257 0.2564 0.1097 0.7413 0.2703 0.8620 0.1476 0.6110 0.0680 0.0358 0.6444 0.6135 0.0636 0.5201 0.1971 0.9899 0.0550Columns 31 through 400.8507 0.7386 0.5523 0.1239 0.7378 0.5590 0.1781 0.8949 0.6311 0.6925 0.5606 0.5860 0.6299 0.4904 0.0634 0.8541 0.3596 0.0715 0.0899 0.5567 0.9296 0.2467 0.0320 0.8530 0.8604 0.3479 0.0567 0.2425 0.0809 0.3965 0.6967 0.6664 0.6147 0.8739 0.9344 0.4460 0.5219 0.0538 0.7772 0.0616 0.5828 0.0835 0.3624 0.2703 0.9844 0.0542 0.3358 0.4417 0.9051 0.78020.8154 0.6260 0.0495 0.2085 0.8589 0.1771 0.1757 0.0133 0.5338 0.33760.8790 0.6609 0.4896 0.5650 0.7856 0.6628 0.2089 0.8972 0.1092 0.60790.9889 0.7298 0.1925 0.6403 0.5134 0.3308 0.9052 0.1967 0.8258 0.74130.0005 0.8908 0.1231 0.4170 0.1776 0.8985 0.6754 0.0934 0.3381 0.10480.8654 0.9823 0.2055 0.2060 0.3986 0.1182 0.4685 0.3074 0.2940 0.12790.6126 0.7690 0.1465 0.9479 0.1339 0.9884 0.9121 0.45610.7463 0.54950.9900 0.5814 0.1891 0.0821 0.0309 0.5400 0.1040 0.1017 0.0103 0.48520.5277 0.9283 0.0427 0.1057 0.9391 0.7069 0.7455 0.9954 0.0484 0.89050.4795 0.5801 0.6352 0.1420 0.3013 0.9995 0.7363 0.3321 0.6679 0.79900.8013 0.0170 0.2819 0.1665 0.2955 0.2878 0.5619 0.2973 0.6035 0.73430.2278 0.1209 0.5386 0.6210 0.3329 0.4145 0.1842 0.0620 0.5261 0.05130.4981 0.8627 0.6952 0.5737 0.4671 0.4648 0.5972 0.2982 0.7297 0.07290.9009 0.4843 0.4991 0.0521 0.6482 0.7640 0.2999 0.0464 0.7073 0.08850.5747 0.8449 0.5358 0.9312 0.0252 0.8182 0.1341 0.5054 0.7814 0.79840.8452 0.2094 0.4452 0.7287 0.8422 0.1002 0.2126 0.7614 0.2880 0.9430Columns 41 through 500.6837 0.7894 0.1123 0.6733 0.0986 0.9879 0.5975 0.7593 0.8092 0.75190.1321 0.3677 0.7844 0.4296 0.1420 0.1704 0.3353 0.7406 0.7486 0.22870.7227 0.2060 0.2916 0.4517 0.1683 0.2578 0.2992 0.7437 0.1202 0.06420.1104 0.0867 0.6035 0.6099 0.1962 0.3968 0.4526 0.1059 0.5250 0.76730.1175 0.7719 0.9644 0.0594 0.3175 0.0740 0.4226 0.6816 0.3258 0.67120.6407 0.2057 0.4325 0.3158 0.3164 0.6841 0.3596 0.4633 0.5464 0.71520.3288 0.3883 0.6948 0.7727 0.2176 0.4024 0.5583 0.2122 0.3989 0.64210.6538 0.5518 0.7581 0.6964 0.2510 0.9828 0.7425 0.0985 0.4151 0.41900.7491 0.2290 0.4326 0.1253 0.8929 0.4022 0.4243 0.8236 0.1807 0.39080.5832 0.6419 0.6555 0.1302 0.7032 0.6207 0.4294 0.1750 0.2554 0.81610.7400 0.4845 0.1098 0.0924 0.5557 0.1544 0.1249 0.1636 0.0205 0.31740.2348 0.1518 0.9338 0.0078 0.1844 0.3813 0.0244 0.6660 0.9237 0.81450.7350 0.7819 0.1875 0.4231 0.2120 0.1611 0.2902 0.8944 0.6537 0.78910.9706 0.1006 0.2662 0.6556 0.0773 0.7581 0.3175 0.5166 0.9326 0.85230.8669 0.2941 0.7978 0.7229 0.9138 0.8711 0.6537 0.7027 0.1635 0.50560.0862 0.2374 0.4876 0.5312 0.7067 0.3508 0.9569 0.1536 0.9211 0.63570.3664 0.5309 0.7690 0.1088 0.5578 0.6855 0.9357 0.9535 0.7947 0.95090.3692 0.0915 0.3960 0.6318 0.3134 0.2941 0.4579 0.5409 0.5774 0.44400.6850 0.4053 0.2729 0.1265 0.1662 0.5306 0.2405 0.6797 0.4400 0.06000.5979 0.1048 0.0372 0.1343 0.6225 0.8324 0.7639 0.0366 0.2576 0.8667 2.参考课本综合例题2.5.4和2.5.5中的方法，模拟产生1000个随机变量，使其服从参数为2的指数分布，进而计算这1000个随机数的均值和方差。

大连理工大学矩阵与数值分析上机作业代码

大连理工大学矩阵与数值分析上机作业代码

则方程组有解 x = (1,1,⋯ ,1) 。 对 n = 10 和 n = 84 ， 分别用 Gauss 消去法和列主元消去法解
T
方程组，并比较计算结果。
1.1 程序
（1）高斯消元法 n=10 时， >> [A,b]=CreateMatrix(10) A= 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6 8 0 0 0 0 0 0 0 0 1 6
1.3 M 文件
.m 1.3.1 CreateMatrix CreateMatrix.m function [A,b]=CreateMatrix(n) %用于存放习题1的题目信息，并建立构造题目中矩阵的函数 %对矩阵A赋值 A1=6*ones(1,n); A2=ones(1,n-1); A3=8*ones(1,n-1); A=diag(A1)+diag(A2,1)+diag(A3,-1); %对向量b赋值 b=15*ones(n,1); b(1)=7; b(n)=14;
10
，迭代次数上限取默认值
50，使用 Jacobi 法进行迭代。 >> test2 >> b=ones(20,1) >> x0=zeros(20,1) >> [x,n]=JacobiMethod(A,b,x0) x= 0.2766 0.2327 0.2159 0.2223 0.2227 0.2221 0.2222 0.2222 0.2222 0.2222 0.2222 0.2222 0.2222 0.2222 0.2221 0.2227 0.2223 0.2159 0.2327 0.2766
大连理工大学线代上机

大连理工大学线代上机

软1414 叶秀云201492015 上机报告上机作业一Trial>> A=round(5*rand(5))B=round(5*rand(5))C=round(5*rand(5))b=round(5*rand(5,1))A+BA-BA*B+B*Ainv(A)*binv(A)rank(A)det(B)inv(B)rank(B)inv(A*B)rank(A*B)(B')*(A')inv(A*B)inv(B)*inv(A)inv(A)*C*inv(B)A =4 0 1 1 35 1 5 2 01 3 5 5 45 5 2 4 53 545 3B =4 4 4 2 24 0 3 2 22 1 2 4 33 0 54 41 0 0 1 4C =1 2 4 5 43 5 1 3 13 2 3 1 41 3 3 1 11 1 4 1 5b =21132ans =8 4 5 3 59 1 8 4 23 4 7 9 78 5 7 8 94 5 4 6 7 ans =0 -4 -3 -1 11 12 0 -2-1 2 3 1 12 5 -3 0 12 5 4 4 -1 ans =80 53 79 69 7175 54 74 77 7589 51 85 97 102110 77 111 113 12379 41 79 80 80ans =0.4754-0.3197-0.59840.9672-0.0902ans =0.3197 -0.0164 -0.2541 -0.2049 0.3607-0.8443 0.2869 0.1967 0.8361 -0.8115 -0.7213 0.4344 0.4836 0.6803 -1.05741.4262 -0.6885 -0.6721 -1.60662.1475-0.3279 0.1066 0.4016 0.5820 -0.8443 ans =5ans =418.0000ans =-0.0144 0.4354 0.0574 -0.2727 0.01910.2321 -0.2057 0.0718 -0.0909 0.02390.0718 -0.1770 -0.2871 0.3636 -0.0957-0.1100 0.0048 0.4402 -0.0909 -0.18660.0311 -0.1100 -0.1244 0.0909 0.2919 ans =5ans =-0.8088 0.3399 0.3081 0.8553 -1.02110.0586 0.0335 0.0060 -0.0108 -0.04070.9295 -0.4372 -0.4747 -0.9979 1.3348-0.4252 0.2371 0.2279 0.3635 -0.54670.2265 -0.1176 -0.0336 -0.1592 0.1809 ans =5ans =24 40 45 61 5817 25 9 22 1623 43 48 59 6019 40 52 49 5527 35 59 62 60ans =-0.8088 0.3399 0.3081 0.8553 -1.02110.0586 0.0335 0.0060 -0.0108 -0.04070.9295 -0.4372 -0.4747 -0.9979 1.3348-0.4252 0.2371 0.2279 0.3635 -0.54670.2265 -0.1176 -0.0336 -0.1592 0.1809 ans =-0.8088 0.3399 0.3081 0.8553 -1.02110.0586 0.0335 0.0060 -0.0108 -0.04070.9295 -0.4372 -0.4747 -0.9979 1.3348-0.4252 0.2371 0.2279 0.3635 -0.54670.2265 -0.1176 -0.0336 -0.1592 0.1809 ans =-0.0497 -0.5353 -0.0060 0.6289 0.12910.3583 1.0632 0.4029 -1.7332 -0.66080.4518 1.2872 0.8731 -2.1207 -0.6844-0.7394 -2.4091 -1.6491 4.0507 1.62510.2658 0.7208 0.5187 -1.1788 -0.5129 Trial>>上机作业二Trial>> A=rand(4)B=rand(4)C=rand(4)D=rand(4)Z=[A,B;C,D]det(Z)det(A*D-C*B)A=diag([rand rand rand rand])C=diag([rand rand rand rand])Z=[A,B;C,D]det(Z)det(A*D-C*B)A =0.9027 0.3377 0.7803 0.09650.9448 0.9001 0.3897 0.13200.4909 0.3692 0.2417 0.94210.4893 0.1112 0.4039 0.9561B =0.5752 0.8212 0.6491 0.54700.0598 0.0154 0.7317 0.29630.2348 0.0430 0.6477 0.74470.3532 0.1690 0.4509 0.1890C =0.6868 0.7802 0.4868 0.50850.1835 0.0811 0.4359 0.51080.3685 0.9294 0.4468 0.81760.6256 0.7757 0.3063 0.7948D =0.6443 0.3507 0.6225 0.47090.3786 0.9390 0.5870 0.23050.8116 0.8759 0.2077 0.84430.5328 0.5502 0.3012 0.1948Z =0.9027 0.3377 0.7803 0.0965 0.5752 0.8212 0.6491 0.54700.9448 0.9001 0.3897 0.1320 0.0598 0.0154 0.7317 0.29630.4909 0.3692 0.2417 0.9421 0.2348 0.0430 0.6477 0.74470.4893 0.1112 0.4039 0.9561 0.3532 0.1690 0.4509 0.18900.6868 0.7802 0.4868 0.5085 0.6443 0.3507 0.6225 0.47090.1835 0.0811 0.4359 0.5108 0.3786 0.9390 0.5870 0.23050.3685 0.9294 0.4468 0.8176 0.8116 0.8759 0.2077 0.84430.6256 0.7757 0.3063 0.7948 0.5328 0.5502 0.3012 0.1948 ans =-0.0232ans =0.0161A =0.2259 0 0 00 0.1707 0 00 0 0.2277 00 0 0 0.4357C =0.3111 0 0 00 0.9234 0 00 0 0.4302 00 0 0 0.1848Z =0.2259 0 0 0 0.5752 0.8212 0.6491 0.54700 0.1707 0 0 0.0598 0.0154 0.7317 0.29630 0 0.2277 0 0.2348 0.0430 0.6477 0.74470 0 0 0.4357 0.3532 0.1690 0.4509 0.18900.3111 0 0 0 0.6443 0.3507 0.6225 0.47090 0.9234 0 0 0.3786 0.9390 0.5870 0.23050 0 0.4302 0 0.8116 0.8759 0.2077 0.84430 0 0 0.1848 0.5328 0.5502 0.3012 0.1948 ans =7.3868e-04ans =7.3868e-04Trial>>上机作业三N=201492015;a=15;b=49;c=01;d=41;e=21;f=95;g=45;Trial>> h=90;Trial>> A=[a,b,c,d,3,4;1,2,3,4,4,3;12,15,22,17,5,7;e,f,g,h,8,0]; Trial>> B=rref(A)B =1.0000 0 0 0 0.4130 0.95680 1.0000 0 0 -1.7984 -1.49040 0 1.0000 0 -0.3796 -0.37590 0 0 1.0000 2.0806 1.5380N=201492015;a=15;b=49;c=01;d=41;e=21;f=95;g=45;Trial>> h=90;Trial>> A=[a,b,c,d,3,4;1,2,3,4,4,3;12,15,22,17,5,7;e,f,g,h,8,0]; Trial>> B=rref(A)B =1.0000 0 0 0 0.4130 0.95680 1.0000 0 0 -1.7984 -1.49040 0 1.0000 0 -0.3796 -0.37590 0 0 1.0000 2.0806 1.5380上机作业四Trial>> b1=[1,1.9,f,c];Trial>> b2=[1,1.8,f,c];Trial>> A1=[a,b,c,d;0.5,1,1.5,2;12,15,22,17;e,f,g,h];Trial>> A2=[a,b,c,d;0.3,0.6,0.9,1.2;12,15,22,17;e,f,g,h];Trial>> A3=[a,b,c,d;0.1,0.2,0.3,0.4;12,15,22,17;e,f,g,h];Trial>> A4=[a,b,c,d;0.05,0.1,0.15,0.2;12,15,22,17;e,f,g,h];Trial>> x1=A1/b1 x1 =0.02700.01630.23780.5057 Trial>> x2=A2/b1 x2 =0.02700.00980.23780.5057 Trial>> x3=A4/b1 x3 =0.02700.00160.23780.5057 Trial>> x4=A4/b1 x4 =0.02700.00160.23780.5057 Trial>> x5=A1/b2 x5 =0.02650.01630.23760.5046Trial>> x6=A2/b2x6 =0.02650.00980.23760.5046Trial>> x7=A3/b2x7 =0.02650.00330.23760.5046Trial>> x8=A4/b2x8 =0.02650.00160.23760.5046Trial>>上机作业五a1=rand(5,1)a2=rand(5,1)a3=rand(5,1)a4=rand(5,1)a5=rand(5,1)A=[a1,a2,a3,a4,a5]orth(A)a1 =0.90490.97970.43890.11110.2581 a2 =0.40870.59490.26220.60280.7112 a3 =0.22170.11740.29670.31880.4242 a4 =0.50790.08550.26250.80100.0292 a5 =0.92890.73030.48860.57850.2373A =0.9049 0.4087 0.2217 0.5079 0.92890.9797 0.5949 0.1174 0.0855 0.73030.4389 0.2622 0.2967 0.2625 0.48860.1111 0.6028 0.3188 0.8010 0.57850.2581 0.7112 0.4242 0.0292 0.2373 ans =-0.5932 -0.1881 -0.4330 0.1909 -0.6235 -0.5319 -0.5286 0.1934 -0.5094 0.3752 -0.3288 0.0079 -0.0670 0.7395 0.5835 -0.4137 0.8042 -0.1828 -0.3450 0.1723 -0.2931 0.1960 0.8586 0.1953 -0.3167Trial>>上机作业六Trial>> A=rand(5)eig(A)[d,v]=eig(A)x=rand(5,1)eig(x*x')A =0.4588 0.4889 0.9880 0.0987 0.72120.9631 0.6241 0.0377 0.2619 0.10680.5468 0.6791 0.8852 0.3354 0.65380.5211 0.3955 0.9133 0.6797 0.49420.2316 0.3674 0.7962 0.1366 0.7791 ans =2.6238 + 0.0000i0.0391 + 0.2666i0.0391 - 0.2666i0.2420 + 0.0000i0.4829 + 0.0000id =-0.4582 + 0.0000i -0.4322 + 0.1366i -0.4322 - 0.1366i 0.1428 + 0.0000i 0.2020 + 0.0000i-0.3197 + 0.0000i 0.7401 + 0.0000i 0.7401 + 0.0000i -0.6192 + 0.0000i 0.3539 + 0.0000i-0.5143 + 0.0000i -0.0341 - 0.3116i -0.0341 + 0.3116i -0.2603 + 0.0000i -0.0520 + 0.0000i-0.5266 + 0.0000i 0.0473 + 0.2327i 0.0473 - 0.2327i 0.1237 + 0.0000i -0.9110 + 0.0000i-0.3821 + 0.0000i -0.2604 + 0.1558i -0.2604 - 0.1558i 0.7164 + 0.0000i -0.0373 + 0.0000iv =2.6238 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0391 + 0.2666i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0000 + 0.0000i 0.0391 - 0.2666i 0.0000 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.2420 + 0.0000i 0.0000 + 0.0000i0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.4829 + 0.0000i上机作业七A=[1,3/2,0;3/2,-1,1;0,1,1]rref(A)eig(A)B=[1,0,2;0,-1,-2;2,-2,0]rref(B)eig(B)A =1.0000 1.5000 01.5000 -1.0000 1.00000 1.0000 1.0000ans =1 0 00 1 00 0 1ans =-2.06161.00002.0616B =1 0 20 -1 -22 -2 0ans =1 0 20 1 20 0 0ans =-3.0000-0.00003.0000Trial>>上机作业八Trial>> A=[0.7,0.2,0.1;0.2,0.7,0.1;0.1,0.1,0.8]P0=[15;9;6]A =0.7000 0.2000 0.10000.2000 0.7000 0.10000.1000 0.1000 0.8000 P0 =1596Trial>> A*P0ans =12.90009.90007.2000Trial>> A*A*P0ans =11.730010.23008.0400Trial>> A*A*A*A*A*P0ans =10.429910.24249.3277Trial>>。

大连理工矩阵上机作业

大连理工矩阵上机作业

第一题Lagrange插值函数function y=lagrange(x0,y0,x);n=length(x0);m=length(x);for i=1:mz=x(i);s=0.0;for k=1:np=1.0;for j=1:nif j~=kp=p*(z-x0(j))/(x0(k)-x0(j));endends=p*y0(k)+s;endy(i)=s;endx0=[1:10];y0=[67.052,68.008,69.803,72.024,73.400,72.063,74.669,74.487,74.065,76 .777];lagrange(x0,y0,17)ans=-1.9516e+12x=[1:0.1:10];x=x';plot(x0,y0,'r');hold onplot(x,y,'k');legend('原函数','拟合函数')拟合图像如下拟合函数出现了龙格现象，运用多项式进行插值拟合时，效果并不好，高次多项式会因为误差的不断累积，导致龙格现象的发生。

第二题function fun =nihe(n)m=[67.052*10^6,68.008*10^6,69.803*10^6,72.024*10^6,73.400*10^6,72.063 *10^6,74.669*10^6,74.487*10^6,74.065*10^6,76.777*10^6];w=[1,2,3,4,5,6,7,8,9,10];d1=0;d2=0;d3=0;y1=polyfit(m,w,1);y2=polyfit(m,w,2);y3=polyfit(m,w,3);y2=poly2sym(s2);y3=poly2sym(s3);y4=poly2sym(s4);f1=subs(y1,17);f2=subs(y2,17);f3=subs(y3,17);for p=1:10;d1=d1+(subs(y1,w(p))-m(p))^2;d2=d2+(subs(y2,w(p))-m(p))^2;d3=d3+(subs(y3,w(p))-m(p))^2;endd1=sqrt(d1);d2=sqrt(d2);d3=sqrt(d3);fun=[f1 f2 f3;d2 d3 d4];return;结果三次函数的均方误差最小，拟合的最好。