Householder Algorithm finding Q

Question

Frederick Melanson 2021-3-8

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/766721-householder-algorithm-finding-q

回答： Athul Prakash 2021-3-12

Hi, i have this algorithm:

function [Q,R] = householder(A)
   % Write your code here.
   [m,n]=size(A);
   Q=eye(m);
for k=1:n
    z = -sign(A(k,k))*norm(A(k:m,k));
    v = [zeros(k-1,1); A(k,k)-z; A(k+1:m,k)];
    f = v'*v;
    if f == 0, continue; end
for j = k:n
     c = v'*A(:,j); 
     A(:,j) = A(:,j)-(2*c/f)*v; 
end
end
R=A;
end

I get the correct R matrix, but I can't seem to find Q correctly. Please let me know ASAP

2 个评论
显示无隐藏无

Jan 2021-3-9

编辑：Jan 2021-3-9

Terms like "ASAP" are not appropriate, if you ask voluntary members of an internet forum to help you.

What did you try to determine Q?

Frederick Melanson 2021-3-9

I added an extra forloop at the end like this:

for j=k:m

c = v'*Q(:,j);

Q(:,j) = Q(:,j)-(2*c/f)*v;

end

Q=Q';

I get the lower triangular part of Q correctly, the problem is with the upper half of the matrix

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Athul Prakash 2021-3-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/766721-householder-algorithm-finding-q#answer_645768

在 MATLAB Online 中打开

Hi Frederick,

You may prefer the MATLAB built-in qr() function.

[Q,R] = qr(M);

See this documentation:

https://in.mathworks.com/help/matlab/ref/qr.html

Alternately, you may search the Mathworks File Exchange for alternate implementations of Householder algorithm. For example:

https://in.mathworks.com/matlabcentral/fileexchange/72766-qr-decomposition

These are submissions by other MATLAB users, and not part of the MATLAB product. It is not tested or qualified by Mathworks, so use at your own responsibility.