relative error not working properly

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Ifechukwu 2014-7-27

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/143543-relative-error-not-working-properly

评论： Star Strider 2014-7-27

I wrote this function

function [L,U,P,x]=LU_pivot(A,b)
% LU factorization with partial (row) pivoting
[n,n]=size(A);
 x = zeros(n,1);
 L=eye(n);
 P=L;
 U=A;
for k=1:n
    [pivot m]=max(abs(U(k:n,k)));
    m =m+k-1;
    if m~=k
        % interchange rows m and k in U
        temp=U(k,:);
        U(k,:)=U(m,:);
        U(m,:)=temp;
        % interchange rows m and k in P
        temp=P(k,:);
        P(k,:)=P(m,:);
        P(m,:)=temp;
        if k >= 2
            temp=L(k,1:k-1);
            L(k,1:k-1)=L(m,1:k-1);
            L(m,1:k-1)=temp;
        end
    end
    for j=k+1:n
        L(j,k)=U(j,k)/U(k,k); %multipliers
        U(j,:)=U(j,:)-L(j,k)*U(k,:); %rows
    end
y=zeros(m,1); % initiation for y 
y(1)=b(1)/L(1,1);
for i=2:m
   %y(i)=B(i)-L(i,1)*y(1)-L(i,2)*y(2)-L(i,3)*y(3);
    y(i)=-L(i,1)*y(1);
      for k=2:i-1
          y(i)=y(i)-L(i,k)*y(k);
      end;
      y(i)=(b(i)+y(i))/L(i,i);
end;
% Now we use this y to solve Ux = y
x=zeros(m,1);
x(m)=y(m)/U(m,m);
i=m-1;
q=0;
while  (i~= 0)
  x(i)=-U(i,m)*x(m);
   q=i+1;
      while (q~=m)
          x(i)=x(i)-U(i,q)*x(q);
          q=q+1;
      end;
    x(i)=(y(i)+x(i))/U(i,i);
    i=i-1;
end; 
end

Then I wrote this Script

n=input ('size of the system....>');
A= 10*rand(n,n);
z=10*rand(n,1);
b=zeros(n,1);
b= A*z;
[L,U,P,x]=LU_pivot(A,b);
relerr = norm(x-z)/norm(z)

But my relative error isn't working correctly please what's the problem

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Star Strider 2014-7-27

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