relative error not working properly

3 次查看（过去 30 天）
Ifechukwu
Ifechukwu 2014-7-27
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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