Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reorthogonalized Block Classical Gram--Schmidt   A new reorthogonalized block classical Gram--Schmidt algorithm is proposed
that factorizes a full column rank matrix $A$ into $A=QR$ where $Q$ is left
orthogonal (has orthonormal columns) and $R$ is upper triangular and
nonsingular.
  With appropriate assumptions on the diagonal blocks of $R$, the algorithm,
when implemented in floating point arithmetic with machine unit $\macheps$,
produces $Q$ and $R$ such that $\| I- Q^{T} Q \|_2 =O(\macheps)$ and $\| A-QR
\|_2 =O(\macheps \| A \|_2)$. The resulting bounds also improve a previous
bound by Giraud et al. [Num. Math., 101(1):87-100,\ 2005] on the CGS2 algorithm
originally developed by Abdelmalek [BIT, 11(4):354--367,\ 1971].
  \medskip Keywords: Block matrices, Q--R factorization, Gram-Schmidt process,
Condition numbers, Rounding error analysis.

13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: eess
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nlin
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The categories of this paper are: q-alg
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The categories of this paper are: physics
36
The categories of this paper are: cmp-lg