# Questions tagged [qr]

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### Products of the Householder matrices during QR decomposition

It is often said that there is no need to form the Householder matrix during QR decomposition, however I fail to see how to "manage" the product of $n$ Householder matrixes and the matrix $A$...
• 317
1 vote
92 views

### accuracy problem for a null space calculation on a sparse rectangular matrix

I have been using the QR-based approach on this link to find the null space of rectangular matrices, and possibly sparse matrices, that emerge as a result of some coupling conditions of different ...
• 131
101 views

### Updating QR decomposition for geometrically similar least squares problem

Let's say we have a weighted least squares problem under the same matrix $A$ such that, $$\hat{x} := \arg \min_x ||A x - b||_{W_1}$$ where $|| \cdot ||_{W_1}$ is the Euclidean norm weighted by ...
1 vote
196 views

### QR algorithm for eigenvalues and eigenvectors of large symmetric matrices

I am trying to write a QR algorithm in Python for eigenvectors and eigenvalues finding for large symmetric matrices, My initial thought was to use Householder transformation with a Wilkinson shift on ...
• 11
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### Householder Vector algorithm in Golub and Van Loan

(This is repost of a question first asked on Mathematics. Hopefully there are more people here who have a copy of Golub and Van Loan to hand) In the 4th edition of "Matrix Computations", ...
146 views

### qr-algorithm to find eigenvalues not returning expected values

I tried to compute eigen values with the QR-algorithm found here (there is also a wikipedia page also) ...
• 183
1 vote
Let $U \in \mathbb{C}^{m \times n_U}$ be an orthonormal matrix, let $A \in \mathbb{C}^{m \times n_A}$, and $m \geq n_U + n_A$. I want to compute a QR factorization $X = \left[U A\right] = QR$, with \$Q ...