Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Householder orthogonalization with a non-standard inner product   Householder orthogonalization plays an important role in numerical linear
algebra. It attains perfect orthogonality regardless of the conditioning of the
input. However, in the context of a non-standard inner product, it becomes
difficult to apply Householder orthogonalization due to the lack of an initial
orthogonal basis. We propose strategies to overcome this obstacle and discuss
algorithms and variants of Householder orthogonalization with a non-standard
inner product. Rounding error analysis and numerical experiments demonstrate
that our approach is numerically stable.

29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph