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1、矩阵与数值分析上机实习题王安然（）工具：matlab1.（1）（2）Sn1=single(0);%存储(1)问的结果Sn2=single(0);%存储(2)问的结果N=10^2;%输入值分别为10^2,10^4,10^6fori=2:NSn1=Sn1+1/(i^2-1);end;fori=N:-1:2Sn2=Sn2+1/(i^2-1);end;（3）N分别取102,103,104结果如下（4）该题说明，改变元素和的相加顺序影响极限值。计算机中存在大小数相加的舍入误差误差。方法二的方法要比方法一要好，因
2、为避免了大数吃小数的舍入误差。2.x=23;A=[7;3;-5;11];m=size(A);count=(m-1:-1:0);%多项式次数向量f=A'*x.^count';3.%initializationA=[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
3、,-30,41,0,0;0,0,0,0,-5,0,0,27,-2;0,0,0,-9,0,0,0,-2,29];b=[-15;27;-23;0;-20;12;-7;7;10];if(det(A)==0)disp('NoUniqueSolution');return;end;m=size(A,1);%GuassianEliminationaug=[A,b];fori=1:mforj=i+1:maug(j,:)=aug(j,:)-aug(j,i)/aug(i,i)*aug(i,:);end;end;disp
4、(aug)x_GaussElim=solveFun(aug);fprintf('xforGuassianElimination');disp(x_GaussElim);%GuassianColumnPCAaug1=[A,b];fori=1:mmax=aug1(i,i);flag=i;fork=i+1:mif(aug1(k,i)^2>max^2)max=aug1(k,i);flag=k;end;end;temp=aug1(flag,:);aug1(flag,:)=aug1(i,:);aug1(i,:
5、)=temp;forj=i+1:maug1(j,:)=aug1(j,:)-aug1(j,i)/aug1(i,i)*aug1(i,:);end;end;x_GaussColu=solveFun(aug1);fprintf('xforGaussianColumnPCA');disp(x_GaussColu)其中解上三角方程组的函数solveFun（aug）:functionx=solveFun(ang)n=size(ang,1);x=zeros(n,1);A=ang(:,1:n);Y=ang(:,n+
6、1);x(n,1)=Y(n,1)/A(n,n);fori=n-1:-1:1x(i,1)=(Y(i,1)-A(i,i+1:n)*x(i+1:n,1))/A(i,i);end;disp(x);4.%LUfunction[L,U]=LU(A)m=size(A,1);%LUA1=A;L=eye(m);fori=1:ml=eye(m);forj=i+1:ml(j,i)=-A1(j,i)/A1(i,i);end;A1=l*A1;L=L*l^(-1);end;U=A1;fprintf('L:');disp(L)
7、;fprintf('U:');disp(U);end%A_inversefunctionA_inverse=LU_inverse(A)[L,U]=LU(A);n=size(A,1);L_inv=zeros(n,n);U_inv=zeros(n,n);%inv(L)fori=1:1:nL_inv(i,i)=1/L(i,i);endfori=2:1:nforj=1:1:i-1L_inv(i,j)=-L_inv(i,i)*(L(i,j:(i-1))*L_inv(j:(i-1),j));endend%in
8、v(U)fori=1:1:nU_inv(i,i)=1/U(i,i);endfori=1:1:n-1k=1;forj=i+1:1:nU_inv(k,j)=-U_inv(k,k)*(U(k,(k+1):j)*U_inv((k+1):j,j));k=k+1;endendA_inverse=L_inv*U_inv;fprintf('A_inverse');disp(A_inverse);end%A_detfunctionA_det=LU_det(A)m=si
