Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Method for Computing $\varphi$-functions and Their Condition
  Numbers of Large Sparse Matrices   We propose a new method for computing the $\varphi$-functions of large sparse
matrices with low rank or fast decaying singular values. The key is to reduce
the computation of $\varphi_{\ell}$-functions of a large matrix to
$\varphi_{\ell+1}$-functions of some $r$-by-$r$ matrices, where $r$ is the
numerical rank of the large matrix in question. Some error analysis on the new
method is given. Furthermore, we propose two novel strategies for estimating
2-norm condition numbers of the $\varphi$-functions. Numerical experiments
illustrate the numerical behavior of the new algorithms and show the
effectiveness of our theoretical results.

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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
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The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat