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Householder Algorithm finding Q

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Frederick Melanson
Frederick Melanson on 8 Mar 2021
Answered: Athul Prakash on 12 Mar 2021
Hi, i have this algorithm:
function [Q,R] = householder(A)
% Write your code here.
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;
I get the correct R matrix, but I can't seem to find Q correctly. Please let me know ASAP
Jan on 9 Mar 2021
Edited: Jan on 9 Mar 2021
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
Frederick Melanson on 9 Mar 2021
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;
I get the lower triangular part of Q correctly, the problem is with the upper half of the matrix

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Answers (1)

Athul Prakash
Athul Prakash on 12 Mar 2021
Hi Frederick,
You may prefer the MATLAB built-in qr() function.
[Q,R] = qr(M);
See this documentation:
Alternately, you may search the Mathworks File Exchange for alternate implementations of Householder algorithm. For example:
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.


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