Questions tagged [householder]
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3
questions
3
votes
1answer
95 views
Efficient solution to a structured symmetric linear system with condition number estimation
I have a real-valued linear system $Hx = b$ where $H$ is symmetric matrix** (not necessarily positive/negative definite) with a very particular structure:
$$
H = \begin{bmatrix} D && B \\ B^T &...
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votes
0answers
153 views
How to implement the gmres method using Householder transformation instead of the Gram-Schmidt?
For Generalized Minimal Residual method GMRES, we usually use the Modified Gram-Schmidt MGS to generate an orthonormal basis of ...
1
vote
2answers
111 views
Why Householder transformation can not be chosen to be an identity matrix?
For Householder transformation, we know that
$H = I-uu^T$, where $\|u\|_2=\sqrt{2}$. When it acts on any vector $x$, $Hx$ and $x$ is symmetric with respect to $span(u)^T$. But I have read a ...
