187 research outputs found
Linguistic Training And The Teaching Of Languages
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98276/1/j.1467-1770.1958.tb00862.x.pd
Solving Large Sparse Lyapunov Equations on Parallel Computers
Abstract. This paper describes the parallelization of the low-rank ADI iteration for the solution of large-scale, sparse Lyapunov equations. The only relevant operations involved in the method are matrix-vector prod-ucts and the solution of linear systems. Experimental results on a cluster, using the SuperLU library, show the performance of this approach
A bootstrap method for sum-of-poles approximations
A bootstrap method is presented for finding efficient sum-of-poles approximations of causal functions. The method is based on a recursive application of the nonlinear least squares optimization scheme developed in (Alpert et al. in SIAM J. Numer. Anal. 37:1138–1164, 2000), followed by the balanced truncation method for model reduction in computational control theory as a final optimization step. The method is expected to be useful for a fairly large class of causal functions encountered in engineering and applied physics. The performance of the method and its application to computational physics are illustrated via several numerical examples
Structure-preserving tangential interpolation for model reduction of port-Hamiltonian Systems
Port-Hamiltonian systems result from port-based network modeling of physical
systems and are an important example of passive state-space systems. In this
paper, we develop the framework for model reduction of large-scale
multi-input/multi-output port-Hamiltonian systems via tangential rational
interpolation. The resulting reduced-order model not only is a rational
tangential interpolant but also retains the port-Hamiltonian structure; hence
is passive. This reduction methodology is described in both energy and
co-energy system coordinates. We also introduce an -inspired
algorithm for effectively choosing the interpolation points and tangential
directions. The algorithm leads a reduced port-Hamiltonian model that satisfies
a subset of -optimality conditions. We present several numerical
examples that illustrate the effectiveness of the proposed method showing that
it outperforms other existing techniques in both quality and numerical
efficiency
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