In the past decades, Model Order Reduction (MOR) has demonstrated its robustness and
wide applicability for simulating large-scale mathematical models in engineering and the …

In this paper we review the state of affairs in the area of approximation of large-scale
systems. We distinguish three basic categories, namely the {SVD}-based, the {Krylov}-based …

Data-driven discovery is revolutionizing how we model, predict, and control complex
systems. Now with Python and MATLAB®, this textbook trains mathematical scientists and …

In today's technological world, physical and artificial processes are mainly described by
mathematical models, which can be used for simulation or control. These processes are …

Excerpt More than 25 years have passed since the first edition of this book was published in
1996. Least squares and least-norm problems have become more significant with every …

This book, Eigensystems, is the second volume in a projected five-volume series entitled
Matrix Algorithms. The first volume treated basic decompositions. The three following this …

This book, Basic Decompositions, is the first volume in a projected five-volume series
entitled Matrix Algorithms. The other four volumes will treat eigensystems, iterative methods …

An algorithm is presented in this paper for computing state-space balancing transformations
directly from a state-space realization. The algorithm requires no" squaring up" or …

The computation of the singular value decomposition, or SVD, has a long history with many
improvements over the years, both in its implementations and algorithmically. Here, we …

The purpose of this paper is to investigate the problem of iterative computation of
approximately balanced reduced order systems. The resulting approach is completely …