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Padé Approximation Of LargeScale Dynamic Systems With Lanczos Methods
, 1994
"... The utility of Lanczos methods for the approximation of largescale dynamical systems is considered. In particular, it is shown that the Lanczos method is a technique for yielding Pad'e approximants which has several advantages over more traditional explicit moment matching approaches. An extension ..."
Abstract

Cited by 18 (1 self)
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The utility of Lanczos methods for the approximation of largescale dynamical systems is considered. In particular, it is shown that the Lanczos method is a technique for yielding Pad'e approximants which has several advantages over more traditional explicit moment matching approaches. An extension of the Lanczos algorithm is developed for computing multipoint Pad'e approximations of descriptor systems. Keywords: Dynamic system, Pad'e approximation, Lanczos algorithm, model reduction. 1. Introduction This paper explores the use of Lanczos techniques for the reducedorder modeling and simulation of largescale, SISO dynamical systems. One can define such a system through the set of state space equations ae E x(t) = Ax(t) + bu(t) y(t) = cx(t) + du(t): (1) The scalar functions u(t) and y(t) are the system's input and output while x(t) is the state vector of dimension n. For simplicity, the directcoupling term, d, will be assumed to be zero. The system matrix, A 2 R n\Thetan ...
On some modifications of the Lanczos algorithm and the relation with Padé approximations
, 1995
"... In this paper we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. 1 1 Introduction For simplicity we assume here that all systems are SISO, although some results do extend to the MIMO case. Let ..."
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Cited by 5 (0 self)
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In this paper we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. 1 1 Introduction For simplicity we assume here that all systems are SISO, although some results do extend to the MIMO case. Let a nth order dynamical system be described by x = Ax + bu (1.1) y = cx + du (1.2) where A is a square, b is a column vector, c is a row vector, and d is a scalar. It is wellknown that the transfer function of this system : h(s) = c(sI \Gamma A) \Gamma1 b + d has a Taylor expansion around s = 1 that looks like : h(s) = d + cbs \Gamma1 + cAbs \Gamma2 + cA 2 bs \Gamma3 + cA 3 bs \Gamma4 + : : : The coefficients m \Gammai of the powers of s \Gammai satisfy thus m 0 = d ; m \Gammai = cA i\Gamma1 b ; i 1: For i 1 these are also called moments or Markov parameters of the system fA; b; cg. It follows already from the work of Hankel that the first 2n moments 1 To appea...
The Lanczos algorithm and Padé approximations
 Short Course, Benelux Meeting on Systems and Control
, 1995
"... Introduction In these two lectures we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. These notes are based on material in the papers [10, 17, 11, 12] for which a lot of credit ought to be give ..."
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Cited by 4 (0 self)
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Introduction In these two lectures we try to show the relations between the Lanczos algorithm and Pad'e approximations as used e.g. in identification and model reduction of dynamical systems. These notes are based on material in the papers [10, 17, 11, 12] for which a lot of credit ought to be given to the respective coauthors. For simplicity we assume here that all systems are SISO, although some results do extend to the MIMO case. Let a nth order dynamical system be described by x = Ax + bu (1) y = cx + du (2) where A is a square, b is a column vector, c is a row vector, and d is a scalar. It is wellknown that the transfer function of this system : h(s) = c(sI \Gamma A) \Gamma1 b +<F29