2018/04/11 by Jean-Christophe Loiseau, Michele Alessandro Bucci, Loiseau, Jean-Christophe +5
Computer Science · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Matrix Theory and Algorithms #Model Reduction and Neural Networks #Numerical methods for differential equations
paper · doi:10.48550/arxiv.1804.03859
openalex publication_date 2018/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
With the ever increasing computational power available and the development of high-performances computing, investigating the properties of realistic very large-scale nonlinear dynamical systems has been become reachable. It must be noted however that the memory capabilities of computers increase at a slower rate than their computational capabilities. Consequently, the traditional matrix-forming approaches wherein the Jacobian matrix of the system considered is explicitly assembled become rapidly intractable. Over the past two decades, so-called matrix-free approaches have emerged as an efficient alternative. The aim of this chapter is thus to provide an overview of well-grounded matrix-free methods for fixed points computations and linear stability analyses of very large-scale nonlinear dynamical systems.