716 research outputs found
Pseudo-Optimal Reduction of Structured DAEs by Rational Interpolation
In this contribution, we extend the concept of inner product
and pseudo-optimality to dynamical systems modeled by
differential-algebraic equations (DAEs). To this end, we derive projected
Sylvester equations that characterize the inner product in
terms of the matrices of the DAE realization. Using this result, we extend the
pseudo-optimal rational Krylov algorithm for ordinary
differential equations to the DAE case. This algorithm computes the globally
optimal reduced-order model for a given subspace of defined by
poles and input residual directions. Necessary and sufficient conditions for
pseudo-optimality are derived using the new formulation of the
inner product in terms of tangential interpolation conditions.
Based on these conditions, the cumulative reduction procedure combined with the
adaptive rational Krylov algorithm, known as CUREd SPARK, is extended to DAEs.
Important properties of this procedure are that it guarantees stability
preservation and adaptively selects interpolation frequencies and reduced
order. Numerical examples are used to illustrate the theoretical discussion.
Even though the results apply in theory to general DAEs, special structures
will be exploited for numerically efficient implementations
Computational Strategies in Lattice QCD
Lectures given at the Summer School on "Modern perspectives in lattice QCD",
Les Houches, August 3-28, 2009Comment: Latex source, 72 pages, 23 figures; v2: misprints corrected, minor
text change
A numerical comparison of solvers for large-scale, continuous-time algebraic Riccati equations and LQR problems
In this paper, we discuss numerical methods for solving large-scale
continuous-time algebraic Riccati equations. These methods have been the focus
of intensive research in recent years, and significant progress has been made
in both the theoretical understanding and efficient implementation of various
competing algorithms. There are several goals of this manuscript: first, to
gather in one place an overview of different approaches for solving large-scale
Riccati equations, and to point to the recent advances in each of them. Second,
to analyze and compare the main computational ingredients of these algorithms,
to detect their strong points and their potential bottlenecks. And finally, to
compare the effective implementations of all methods on a set of relevant
benchmark examples, giving an indication of their relative performance
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