An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems

An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems In this paper, we propose an extended block Krylov process to construct two biorthogonal bases for the extended Krylov subspaces $$\mathbb {K}_{m}^e(A,V)$$ K m e ( A , V ) and $$\mathbb {K}_{m}^e(A^{T},W)$$ K m e ( A T , W ) , where $$A \in \mathbb {R}^{n \times n}$$ A ∈ R n × n and $$V,~W \in \mathbb {R}^{n \times p}$$ V , W ∈ R n × p . After deriving some new theoretical results and algebraic properties, we apply the proposed algorithm with moment matching techniques for model reduction in large scale dynamical systems. Numerical experiments for large and sparse problems are given to show the efficiency of the proposed method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Calcolo Springer Journals

An extended nonsymmetric block Lanczos method for model reduction in large scale dynamical systems

, Volume 55 (1) – Feb 21, 2018
23 pages

/lp/springer_journal/an-extended-nonsymmetric-block-lanczos-method-for-model-reduction-in-jOEINoymaV
Publisher
Springer Milan
Subject
Mathematics; Numerical Analysis; Theory of Computation
ISSN
0008-0624
eISSN
1126-5434
D.O.I.
10.1007/s10092-018-0248-5
Publisher site
See Article on Publisher Site

Abstract

In this paper, we propose an extended block Krylov process to construct two biorthogonal bases for the extended Krylov subspaces $$\mathbb {K}_{m}^e(A,V)$$ K m e ( A , V ) and $$\mathbb {K}_{m}^e(A^{T},W)$$ K m e ( A T , W ) , where $$A \in \mathbb {R}^{n \times n}$$ A ∈ R n × n and $$V,~W \in \mathbb {R}^{n \times p}$$ V , W ∈ R n × p . After deriving some new theoretical results and algebraic properties, we apply the proposed algorithm with moment matching techniques for model reduction in large scale dynamical systems. Numerical experiments for large and sparse problems are given to show the efficiency of the proposed method.

Journal

CalcoloSpringer Journals

Published: Feb 21, 2018

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