大连理工大学-矩阵大作业.doc

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1、（1）从大到小的顺序的计算程序：functiony=snd(n)formatlongy=0;ifn<2disp('请输入大于1的数！')elses=0;i=2;whilei<=ns=single(s+(1/(i^2-1)));i=i+1;endy=s;end（2）从小到大的顺序的计算程序：functiony=snx(n)formatlongy=0;ifn<2disp('请输入大于1的数！')elses=0;i=n;while1s=single(s+(1/(i^2-1)));i=i-1;ifi==1breakendendy=s;end（3）按两种顺序分别计算并指出有效

2、位数（编制程序时用单精度）①　的计算结果：②　的计算结果：③　的计算结果：计算时的有效位数为七位数。①　秦九昭算法计算程序：functiony=qjz(a,x)j=3;i=size(a,2);switchicase1y=a(1);case2y=a(1)*x+a(2);otherwisep=a(1)*x+a(2);whilej<=ip=p*x+a(j);j=j+1;endy=p;end②　计算在点23的值。计算结果如下：当时。①　Gauss法计算程序和结果：程序：A(1,:)=[31,-13,0,0,0,-10,0,0,0];A(2,:)=[-13,35,-9,0,-

3、11,0,0,0,0];A(3,:)=[0,-9,31,-10,0,0,0,0,0];A(4,:)=[0,0,-10,79,-30,0,0,0,-9];A(5,:)=[0,0,0,-30,57,-7,0,-5,0];A(6,:)=[0,0,0,0,-7,47,-30,0,0];A(7,:)=[0,0,0,0,0,-30,41,0,0];A(8,:)=[0,0,0,0,-5,0,0,27,-2];A(9,:)=[0,0,0,-9,0,0,0,-2,29];B=[-15;27;-23;0;-20;12;-7;7;10];[a,b]=gauss(A,B);j=size(a

4、,2);whilej>=1k=j+1;s=b(j);whilek<=9s=s-x(k)*a(j,k);k=k+1;endx(j)=s/a(j,j);j=j-1;enddisp(x)function[x,y]=gauss(a,b)num_i=size(a,1);j=1;whilej<=(num_i-1)i=j+1;whilei<=num_ir=a(i,j)/a(j,j);a(i,:)=a(i,:)-r*a(j,:);b(i,:)=b(i,:)-r*b(j,:);i=i+1;endj=j+1;endx=a;y=b;运行的结果为：。①　列主元消去法计算程序和结果：A(1,

5、:)=[31,-13,0,0,0,-10,0,0,0];A(2,:)=[-13,35,-9,0,-11,0,0,0,0];A(3,:)=[0,-9,31,-10,0,0,0,0,0];A(4,:)=[0,0,-10,79,-30,0,0,0,-9];A(5,:)=[0,0,0,-30,57,-7,0,-5,0];A(6,:)=[0,0,0,0,-7,47,-30,0,0];A(7,:)=[0,0,0,0,0,-30,41,0,0];A(8,:)=[0,0,0,0,-5,0,0,27,-2];A(9,:)=[0,0,0,-9,0,0,0,-2,29];B=[-15;2

6、7;-23;0;-20;12;-7;7;10];[a,b]=lzy(A,B);j=size(a,2);whilej>=1k=j+1;s=b(j);whilek<=9s=s-x(k)*a(j,k);k=k+1;endx(j)=s/a(j,j);j=j-1;enddisp(x)function[a1,b1]=lzy(a,b)[num_i,num_j]=size(a);ab=zeros(num_i,num_j+1);fork=1:num_jab(:,k)=a(:,k);endab(:,num_j+1)=b(:,1);j=1;whilej

7、searmax(j,j,ab);i_nu=ab(j,:);ab(j,:)=ab(max_i,:);ab(max_i,:)=i_nu;m=j+1;whilem<=num_iforn=j:num_j+1ab(m,n)=ab(m,n)-(ab(m,j)/max)*ab(j,n);endm=m+1;endj=j+1;enda1=zeros(num_i,num_j);fork=1:num_ia1(:,k)=ab(:,k);endb1=ab(:,num_i+1);function[b,c]=searmax(i,j,a)num_i=size(a,1);k=i;m=abs(a(