A model reduction method for large-scale linear multidimensional dynamical systems
Abstract
In this work, we explore the application of multilinear algebra in reducing the order of multidimentional linear time-invariant (MLTI) systems. We use tensor Krylov subspace methods as key tools, which involve approximating the system solution within a low-dimensional subspace. We introduce the tensor extended block and global Krylov subspaces and the corresponding Arnoldi based processes. Using these methods, we develop a model reduction using projection techniques. We also show how these methods could be used to solve large-scale Lyapunov tensor equations that are needed in the balanced truncation method which is a technique for order reduction. We demonstrate how to extract approximate solutions via the Einstein product using the tensor extended block Arnoldi and the extended global Arnoldi processes.
Keywords
Cite
@article{arxiv.2305.09361,
title = {A model reduction method for large-scale linear multidimensional dynamical systems},
author = {M. A. Hamadi and K. Jbilou and A. Ratnani},
journal= {arXiv preprint arXiv:2305.09361},
year = {2023}
}