Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fast Newton-Shamanskii iteration for M/G/1-type and GI/M/1-type Markov
  chains   For the nonlinear matrix equations arising in the analysis of M/G/1-type and
GI/M/1-type Markov chains, the minimal nonnegative solution $G$ or $R$ can be
found by Newton-like methods. Recently a fast Newton's iteration is proposed in
\cite{Houdt2}. We apply the Newton-Shamanskii iteration to the equations.
Starting with zero initial guess or some other suitable initial guess, the
Newton-Shamanskii iteration provides a monotonically increasing sequence of
nonnegative matrices converging to the minimal nonnegative solution. We use the
technique in \cite{houdt2} to accelerate the Newton-Shamanskii iteration.
Numerical examples illustrate the effectiveness of the Newton-Shamanskii
iteration.

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The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: bayes-an