Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the ADI method for the Sylvester Equation and the
  optimal-$\mathcal{H}_2$ points   The ADI iteration is closely related to the rational Krylov projection
methods for constructing low rank approximations to the solution of Sylvester
equation. In this paper we show that the ADI and rational Krylov approximations
are in fact equivalent when a special choice of shifts are employed in both
methods. We will call these shifts pseudo H2-optimal shifts. These shifts are
also optimal in the sense that for the Lyapunov equation, they yield a residual
which is orthogonal to the rational Krylov projection subspace. Via several
examples, we show that the pseudo H2-optimal shifts consistently yield nearly
optimal low rank approximations to the solutions of the Lyapunov equations.

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The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
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The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th