Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: GMRES on singular systems revisited   In [Hayami K, Sugihara M. Numer Linear Algebra Appl. 2011; 18:449--469], the
authors analyzed the convergence behaviour of the Generalized Minimal Residual
(GMRES) method for the least squares problem $ \min_{ {\bf x} \in {\bf R}^n}
{\| {\bf b} - A {\bf x} \|_2}^2$, where $ A \in {\bf R}^{n \times n}$ may be
singular and $ {\bf b} \in {\bf R}^n$, by decomposing the algorithm into the
range $ {\cal R}(A) $ and its orthogonal complement $ {\cal R}(A)^\perp $
components. However, we found that the proof of the fact that GMRES gives a
least squares solution if $ {\cal R}(A) = {\cal R}(A^{\scriptsize T} ) $ was
not complete. In this paper, we will give a complete proof.

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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat