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In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram–Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices… (More)
In this note we present a new updating technique to estimate a low rank approximation of the Hankel map of a time-varying system. We obtain error estimates of our approximation and also explain how to use this for model reduction of time-varying as well as time invariant systems.
We present a benchmark collection containing some useful real world examples, which can be used to test and compare numerical methods for model reduction. All systems can be downloaded from the web and we describe here the relevant characteristics of the benchmark examples.
Linear Algebra and its Applications xx (2004) xxx–xxx Abstract We consider second-order linear time-invariant systems. The objective of this paper is to present a new method for constructing a reduced system by preserving the second-order structure of the original system. This new model reduction method uses a variant of the well-known balanced truncation… (More)
This paper presents new recursive projection techniques to compute reduced order models of time-varying linear systems. The methods produce a low-rank approximation of the gramians or of the Hankel map of the system and are mainly based on matrix operations that can exploit sparsity of the model. We show the practical relevance of our results with a few… (More)
In this paper we present a Smith-like updating technique to estimate a low rank approximation of the Gramians of a time-varying system. We obtain error estimates of our approximation and also explain how to use this for model reduction of time-varying systems.
We describe an algorithm for estimating the H ∞-norm of a large linear time invariant dynamical system described by a discrete time state-space model. The algorithm uses Chandrasekhar iterations to obtain an estimate of the H ∞-norm and then uses extrapolation to improve these estimates. Résumé. Nous décrivons un algorithme pour estimer la norme H ∞ d'un… (More)
In this paper, we construct a global optimization algorithm to compute the H ∞ norm of the transfer matrix of linear dynamic system. The algorithm takes the benefit of the fact that the generalized eigenvalue problem with Hamiltonian or symplectic structure not only gives a finite number of sets of subintervals of real axis among which the global maximum of… (More)