# Householder Reflection QR=A

218 views (last 30 days)
Ismail Güclü on 26 Aug 2020
Answered: Monisha Nalluru on 18 Sep 2020
function [Q,R] = househ(A)
%QR-Zerlegung mit Householder
[m,n]=size(A);
Q = eye(m);
D = eye(m);
p = min(m-1,n);
for k=1:p
%untermatrix erstellen / define sub-matrix
x = A(:,k);
if k == 1
x = A(:,k);
elseif k <= p
for i = 1:(k-1)
x(i) = 0;
end
else
continue
end
%Formeln aus dem Buch / equation of the book
a = -sign(A(k,k))*norm(x);
v = x - a*D(:,k);
H = D-2*(v*v')/(v'*v);
% ---------------------------------
if k == 1
Q=H;
else
Q = Q*H;
end
A=H*A;
end
A(find(A==-0))=0; % unnecessary
R=A;
Q=Q';
end
Here u can see my Householder transformation. The Code under the hyphens is wrong but I don´t know why ... can someone help me.

Monisha Nalluru on 18 Sep 2020
Refer to this blog post which explains on Household Refelection and Household QR factorization with sample code for understanding.

R2020a

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