QR Factorization using Householder Transformation

Question

Mar Cha 2021-3-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/763151-qr-factorization-using-householder-transformation

回答： Monisha Nalluru 2021-3-10

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Hello!

I am trying to compute a function householder that taking a matrix A, returns the matrix Q R such that

This is my code so far but it seems that I have a mistake since

~= A:

Any help please?

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

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Answer 1

Monisha Nalluru 2021-3-10

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/763151-qr-factorization-using-householder-transformation#answer_643997

Refer to the following blog post which gives example and clear understanding on Household Refelection and Household QR factorization with sample code.