Results 1 
4 of
4
Asymptotic waveform evaluation via a Lanczos method
 Appl. Math. Lett
, 1994
"... AbstractIn this paper we show that the twosided Lanczos procedure combined with implicit restarts, offers significant advantages over Pad6 approximations used typically for model reduction in circuit simulation. ..."
Abstract

Cited by 57 (4 self)
 Add to MetaCart
AbstractIn this paper we show that the twosided Lanczos procedure combined with implicit restarts, offers significant advantages over Pad6 approximations used typically for model reduction in circuit simulation.
On some modifications of the Lanczos algorithm and the relation with PadÃ© 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 ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
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 PadÃ© 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 ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
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
Asymptotic Waveform Evaluation via a Restarted Lanczos Method
 Appl. Math. Lett
, 1994
"... this paper, it will be demonstrated that a Pad'e approximation of the original circuit can be obtained without explicitly passing via the moments. Through the nonsymmetric Lanczos method [9, 14], one can realize the reducedorder system f ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
this paper, it will be demonstrated that a Pad'e approximation of the original circuit can be obtained without explicitly passing via the moments. Through the nonsymmetric Lanczos method [9, 14], one can realize the reducedorder system f