Displaying similar documents to “On tropical Kleene star matrices and alcoved polytopes”

Weak regularizability and pole assignment for non-square linear systems

Tetiana Korotka, Jean-Jacques Loiseau, Petr Zagalak (2012)

Kybernetika

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The problem of pole assignment by state feedback in the class of non-square linear systems is considered in the paper. It is shown that the problem is solvable under the assumption of weak regularizability, a newly introduced concept that can be viewed as a generalization of the regularizability of square systems. Necessary conditions of solvability for the problem of pole assignment are established. It is also shown that sufficient conditions can be derived in some special cases. Some...

Efficient application of e-invariants in finite element method for an elastodynamic equation

Martin Balazovjech, Ladislav Halada (2013)

Kybernetika

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We introduce a new efficient way of computation of partial differential equations using a hybrid method composed from FEM in space and FDM in time domain. The overall computational scheme is explicit in time. The key idea of the suggested way is based on a transformation of standard basis functions into new basis functions. The results of this matrix transformation are e-invariants (effective invariants) with such suitable properties which save the number of arithmetical operations needed for a problem solution. The application of this procedure and its effectiveness for 2D problem was the first time published in [2]. Now we describe the generalization of this procedure for 3D problem. In order to present the main principle of our process and its advantage, we first explain the main idea of our approach on a simple 1D example and then the application of the e-invariants on an elastodynamics equation using hexahedral elements in 3D is described. Finally, the efficiency of the suggested method in both cases from the point of the required number of arithmetical operations is analyzed. The result of this analysis confirms computational efficiency the suggested method and the usefulness of e-invariants which save only the essential information needed for the computation. Moreover, the method can be used for various types of elements and equations.

Recursive form of general limited memory variable metric methods

Ladislav Lukšan, Jan Vlček (2013)

Kybernetika

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In this report we propose a new recursive matrix formulation of limited memory variable metric methods. This approach can be used for an arbitrary update from the Broyden class (and some other updates) and also for the approximation of both the Hessian matrix and its inverse. The new recursive formulation requires approximately 4 m n multiplications and additions per iteration, so it is comparable with other efficient limited memory...