Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regular approximate factorization of a class of matrix-function with an
  unstable set of partial indices   From the classic work of Gohberg and Krein (1958), it is well known that the
set of partial indices of a non-singular matrix function may change depending
on the properties of the original matrix. More precisely, it was shown that if
the difference between the larger and the smaller partial indices is larger
than unity then, in any neighborhood of the original matrix function, there
exists another matrix function possessing a different set of partial indices.
As a result, the factorization of matrix functions, being an extremely
difficult process itself even in the case of the canonical factorization,
remains unresolvable or even questionable in the case of a non-stable set of
partial indices. Such a situation, in turn, has became an unavoidable obstacle
to the application of the factorization technique. This paper sets out to
answer a less ambitious question than that of effective factorizing matrix
functions with non-stable sets of partial indices, and instead focuses on
determining the conditions which, when imposed on the original matrix function,
allow to construct another matrix function that exhibits the same partial
indices and is close to the original matrix function.

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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: econ
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci