Abstract:We propose an adaptive model reduction algorithm for computing a reduced-order model of dynamical multi-input and multi-output (MIMO) linear time independent (LTI) dynamical systems. The process is based on multipoint moment matching. Moreover, we develop new simple Lanczos-like equations for the rational block case, and we use them to derive simple residual error expressions. An adaptive method for choosing the interpolation points is also proposed. Finally, some numerical experiments are reported to show the… Show more
“…For this reason, we modified the rational global Lanczos algorithm by allowing some interpolation points to be equal to infinity. Such a result is given in the study of Frangos and Jaimoukha for the standard form and extended to the block case in Barkouki et al The modified rational global Lanczos algorithm is summarized as follows. …”
Section: The Modified Rational Global Lanczos Methodsmentioning
confidence: 99%
“…Recently, some rational Krylov methods were defined; see Grimme and Gallivan et al and the references therein, and it was shown that these rational‐based methods are more effective for model‐order reduction, and also for solving large Lyapunov and Riccati matrix equations . In the next section, we define the rational global Lanczos algorithm and we give some new algebraic properties.…”
Section: Moment Matching‐based Methodsmentioning
confidence: 99%
“…We can produce a reduced model for the second-order system (Equation 29) by applying classical linear model reduction techniques to (, , ) in Equation 34. Unfortunately, there is no guarantee that the resulting reduced system would be a second-order system, which requires the development of second-order structure-preserving model reduction techniques, see other works [48][49][50][51] and the references therein.…”
Section: Model Reduction Of Second-order Systemsmentioning
confidence: 99%
“…Let (, , ) be the state space realization defined in Equation34. If one projects such a state space realization with 2n × 2mp bloc diagonal matrices…”
Summary
In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.
“…For this reason, we modified the rational global Lanczos algorithm by allowing some interpolation points to be equal to infinity. Such a result is given in the study of Frangos and Jaimoukha for the standard form and extended to the block case in Barkouki et al The modified rational global Lanczos algorithm is summarized as follows. …”
Section: The Modified Rational Global Lanczos Methodsmentioning
confidence: 99%
“…Recently, some rational Krylov methods were defined; see Grimme and Gallivan et al and the references therein, and it was shown that these rational‐based methods are more effective for model‐order reduction, and also for solving large Lyapunov and Riccati matrix equations . In the next section, we define the rational global Lanczos algorithm and we give some new algebraic properties.…”
Section: Moment Matching‐based Methodsmentioning
confidence: 99%
“…We can produce a reduced model for the second-order system (Equation 29) by applying classical linear model reduction techniques to (, , ) in Equation 34. Unfortunately, there is no guarantee that the resulting reduced system would be a second-order system, which requires the development of second-order structure-preserving model reduction techniques, see other works [48][49][50][51] and the references therein.…”
Section: Model Reduction Of Second-order Systemsmentioning
confidence: 99%
“…Let (, , ) be the state space realization defined in Equation34. If one projects such a state space realization with 2n × 2mp bloc diagonal matrices…”
Summary
In the present paper, we describe an adaptive modified rational global Lanczos algorithm for model‐order reduction problems using multipoint moment matching‐based methods. The major problem of these methods is the selection of some interpolation points. We first propose a modified rational global Lanczos process and then we derive Lanczos‐like equations for the global case. Next, we propose adaptive techniques for choosing the interpolation points. Second‐order dynamical systems are also considered in this paper, and the adaptive modified rational global Lanczos algorithm is applied to an equivalent state space model. Finally, some numerical examples will be given.
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