Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efficient Solution of Large-Scale Algebraic Riccati Equations Associated
  with Index-2 DAEs via the Inexact Low-Rank Newton-ADI Method   This paper extends the algorithm of Benner, Heinkenschloss, Saak, and
Weichelt: An inexact low-rank Newton-ADI method for large-scale algebraic
Riccati equations, Applied Numerical Mathematics Vol.~108 (2016), pp.~125--142,
doi:10.1016/j.apnum.2016.05.006 to Riccati equations associated with Hessenberg
index-2 Differential Algebratic Equation (DAE) systems. Such DAE systems arise,
e.g., from semi-discretized, linearized (around steady state) Navier-Stokes
equations. The solution of the associated Riccati equation is important, e.g.,
to compute feedback laws that stabilize the Navier-Stokes equations. Challenges
in the numerical solution of the Riccati equation arise from the large-scale of
the underlying systems and the algebraic constraint in the DAE system. These
challenges are met by a careful extension of the inexact low-rank Newton-ADI
method to the case of DAE systems. A main ingredient in the extension to the
DAE case is the projection onto the manifold described by the algebraic
constraints. In the algorithm, the equations are never explicitly projected,
but the projection is only applied as needed. Numerical experience indicates
that the algorithmic choices for the control of inexactness and line-search can
help avoid subproblems with matrices that are only marginally stable. The
performance of the algorithm is illustrated on a large-scale Riccati equation
associated with the stabilization of Navier-Stokes flow around a cylinder.

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The categories of this paper are: bayes-an
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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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: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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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: alg-geom