A partial Padé-via-Lanczos method for reduced-order modeling
نویسندگان
چکیده
The classical Lanczos process can be used to efficiently generate Padé approximants of the transfer function of a given single-input single-output time-invariant linear dynamical system. Unfortunately, in general, the resulting reduced-order models based on Padé approximation do not preserve the stability, and possibly passivity, of the original linear dynamical system. In this paper, we describe the use of partial Padé approximation for reduced-order modeling. Partial Padé approximants have a number of prescribed poles and zeros, while the remaining degrees of freedom are used to match the Taylor expansion of the original transfer function in as many leading coefficients as possible. We present an algorithm for computing partial Padé approximants via suitable rank-1 updates of the tridiagonal matrices generated by the Lanczos process. Numerical results for two circuit examples are reported. © 2001 Elsevier Science Inc. All rights reserved.
منابع مشابه
Padé via Lanczos with Multiple Expansion Points
Through considering a large scale single-input, single-output dynamical linear system, we are led to the task of finding a suitable reduced-order model corresponding to that system. Equivalently, we need to successfully approximate the system’s so-called transfer function. To approximate the transfer function the PVL method considers the Lanczos process and its close knit connection to Padé app...
متن کاملStable and Passive Reduced-order Models Based on Partial Pad E Approximation via the Lanczos Process
This paper describes the use of partial Pad e approximation to generate stable and passive reduced-order models of linear circuits. For similarly-sized models, partial Pad e-based reduced-oreder modeling has superior moment-matching capabilities than competing techniques based on the Arnoldi process. The paper introduces PVL, an algorithm for computing partial Pad e-based reduced-order models v...
متن کاملTranspose-free Multiple Lanczos and Its Application in Padé Approximation
A transpose-free two-sided nonsymmetric Lanczos method is developed for multiple starting vectors on both the left and right. The method is mathematically equivalent to the two-sided methods without look-ahead or deflation steps, but avoids the use of the transpose of the system matrix. The method is applied to the computation of the matrix Padé approximation to a linear dynamical system. The r...
متن کاملError Estimation of the Padé Approximation of Transfer Functions via the Lanczos Process
Krylov subspace based moment matching algorithms, such as PVL (Padé approximation Via the Lanczos process), have emerged as popular tools for efficient analyses of the impulse response in a large linear circuit. In this work, a new derivation of the PVL algorithm is presented from the matrix point of view. This approach simplifies the mathematical theory and derivation of the algorithm. Moreove...
متن کاملModel reduction via an LFT-based explicitly restarted nonsymmetric Lanczos algorithm
The nonsymmetric Lanczos algorithm, which belongs to the class of Krylov subspace methods, is increasingly being used for model reduction of large scale systems of the form f(s) = c (sI−A)−1b, to exploit the sparse structure and reduce the computational burden. However, a good approximation is, usually, achieved only with relatively high order reduced models. Moreover, the computational cost of...
متن کامل