Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balanced Truncation Model Reduction with A Priori Error Bounds for LTI
  Systems with Nonzero Initial Value   In standard balanced truncation model order reduction, the initial condition
is typically ignored in the reduction procedure and is assumed to be zero
instead. However, such a reduced-order model may be a bad approximation to the
full-order system, if the initial condition is not zero. In the literature
there are several attempts for modified reduction methods at the price of
having no error bound or only a posteriori error bounds which are often too
expensive to evaluate. In this work we propose a new balancing procedure that
is based on a shift transformation on the state. We first derive a joint
projection reduced-order model in which the part of the system depending only
on the input and the one depending only on the initial value are reduced at
once and we prove an a priori error bound. With this result at hand, we derive
a separate projection procedure in which the two parts are reduced separately.
This gives the freedom to choose different reduction orders for the different
subsystems. Moreover, we discuss how the reduced-order models can be
constructed in practice. Since the error bounds are parameter-dependent we show
how they can be optimized efficiently. We conclude this paper by comparing our
results with the ones from the literature by a series of numerical experiments.

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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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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: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc