Elena Virnik

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We apply algebraic multigrid (AMG) as a preconditioner for solving large singular linear systems of the type (I−T T)x = 0 with GMRES. Here, T is assumed to be the transition matrix of a Markov process. Although AMG and GMRES are originally designed for the solution of regular systems , with adequate adaptation their applicability can be extended to problems(More)
We propose a model reduction method for positive systems that ensures the positivity of the reduced-order model. In the standard as well as in the descriptor case, for continuous-time and discrete-time systems, our approach is based on constructing diagonal solutions of Lyapunov inequalities. These are linear matrix inequalities (LMIs), which are shown to(More)
We present a new extension of the well-known Perron-Frobenius theorem to regular matrix pairs (E, A). The new extension is based on projector chains and is motivated from the solution of positive differential-algebraic systems or descriptor systems. We present several examples where the new condition holds, whereas conditions in previous literature are not(More)
We apply algebraic multigrid (AMG) as a preconditioner for solving large singular linear systems of the type (I − T T)x = 0 with GMRES. Here, T is assumed to be the transition matrix of a Markov process. Although AMG and GMRES were originally designed for the solution of regular systems, with adequate adaptation their applicability can be extended to(More)
Being one of the key tools in conformation dynamics, the identification of meta-stable states of Markov chains has been subject to extensive research in recent years, especially when the Markov chains represent energy states of biomolecules. Some previous work on this topic involved the computation of the eigenvalue cluster close to one, as well as the(More)
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