Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kalman smoothing and block tridiagonal systems: new connections and
  numerical stability results   The Rauch-Tung-Striebel (RTS) and the Mayne-Fraser (MF) algorithms are two of
the most popular smoothing schemes to reconstruct the state of a dynamic linear
system from measurements collected on a fixed interval. Another (less popular)
approach is the Mayne (M) algorithm introduced in his original paper under the
name of Algorithm A. In this paper, we analyze these three smoothers from an
optimization and algebraic perspective, revealing new insights on their
numerical stability properties. In doing this, we re-interpret classic
recursions as matrix decomposition methods for block tridiagonal matrices.
  First, we show that the classic RTS smoother is an implementation of the
forward block tridiagonal (FBT) algorithm (also known as Thomas algorithm) for
particular block tridiagonal systems. We study the numerical stability
properties of this scheme, connecting the condition number of the full system
to properties of the individual blocks encountered during standard recursion.
Second, we study the M smoother, and prove it is equivalent to a backward block
tridiagonal (BBT) algorithm with a stronger stability guarantee than RTS.
Third, we illustrate how the MF smoother solves a block tridiagonal system, and
prove that it has the same numerical stability properties of RTS (but not those
of M). Finally, we present a new hybrid RTS/M (FBT/BBT) smoothing scheme, which
is faster than MF, and has the same numerical stability guarantees of RTS and
MF.

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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
19
The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
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The categories of this paper are: stat