Related papers: Time-stepping and Krylov methods for large-scale i…
In present paper we suggest a new universal approach to study complex systems by microscopic, mesoscopic and macroscopic methods. We discuss new possibilities of extracting information on nonstationarity, unsteadiness and non-Markovity of…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
Recently, a flexible and stable algorithm was introduced for the computation of 2D unstable manifolds of periodic solutions to systems of ordinary differential equations. The main idea of this approach is to represent orbits in this…
In these lectures notes, we review our recent works addressing various problems of finding the nearest stable system to an unstable one. After the introduction, we provide some preliminary background, namely, defining Port-Hamiltonian…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
An numerical iterative framework for global modal stability analysis of compressible flows using a parallel environment is presented. The framework uses a matrix-free implementation to allow computations of large scale problems. Various…
Assessment of the degree of boundedness/stability of multidimensional nonlinear systems with time-dependent and nonperiodic coefficients is an important problem in various applied areas which has no adequate resolution yet. Most of the…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
The solution of systems of linear(ized) equations lies at the heart of many problems in Scientific Computing. In particular for systems of large dimension, iterative methods are a primary approach. Stationary iterative methods are generally…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
The development of finite/fixed-time stable optimization algorithms typically involves study of specific problem instances. The lack of a unified framework hinders understanding of more sophisticated algorithms, e.g., primal-dual gradient…
Boundary element methods produce dense linear systems that can be accelerated via multipole expansions. Solved with Krylov methods, this implies computing the matrix-vector products within each iteration with some error, at an accuracy…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
For linear inverse problems with a large number of unknown parameters, uncertainty quantification remains a challenging task. In this work, we use Krylov subspace methods to approximate the posterior covariance matrix and describe efficient…
Models coming from different physical applications are very large in size. Simulation with such systems is expensive so one usually obtains a reduced model (by model reduction) that replicates the input-output behaviour of the original full…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
We present some accelerated variants of fixed point iterations for computing the minimal non-negative solution of the unilateral matrix equation associated with an M/G/1-type Markov chain. These variants derive from certain staircase…
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step methods. According to this investigation, we give some…
Our work presents a new iterative scheme to approximate the fixed points of nonexpansive mapping. The proposed algorithm is constructed to enhance convergence efficiency while preserving theoretical robustness. Under appropriate assumptions…
Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…