Publications related to Matrix differential equation

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini, Nicholas Mueller

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Philadelphia2024

CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe

Daniel Garcia Figueroa, Adrien Florio, Wessel Valkenburg, Francisco Torrenti

This paper describes CosmoGattice, a modern package for lattice simulations of the dynamics of interacting scalar and gauge fields in an expanding universe. CosmoGattice incorporates a series of features that makes it very versatile and powerful: i) it is ...

ELSEVIER2023

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

SPRINGER2022

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Julien Gilles Edgar Gateau

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after e ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2020

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

2020

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

Daniel Kressner, Stefano Massei

In this work, we consider two types of large-scale quadratic matrix equations: Continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic proc ...

MATHICSE2019

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

SIAM PUBLICATIONS2019

The time-dependent expected reward and deviation matrix of a finite QBD process

Sophie Myriam Hautphenne

Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of its transient deviation matrix. In this paper we focus on the special case of a finite quasi-birth-and-death (QBD) process, moti ...

ELSEVIER SCIENCE INC2019

Backpropagation-Friendly Eigendecomposition

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition (ED) is widely used in deep networks. However, the backpropagation of its results tends to be numerically unstable, whether using ED directly or approximating it with the Power Iteration method, particularly when dealing with large matri ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2019

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Matrix differential equation

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe

Iterative refinement of Schur decompositions

Electromagnetic waves under nonstationary conditions, the connection with parity-time symmetry and studies on resonant systems

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

The time-dependent expected reward and deviation matrix of a finite QBD process

Backpropagation-Friendly Eigendecomposition

Graph Chatbot

Chat with Graph Search

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Iterative refinement of Schur decompositions

CosmoLattice: A modern code for lattice simulations of scalar and gauge field dynamics in an expanding universe

Electromagnetic waves under nonstationary conditions, the connection with parity-time symmetry and studies on resonant systems

MATHICSE Technical Report : Low-rank updates and divide-andconquer methods for quadratic matrix equations

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

The time-dependent expected reward and deviation matrix of a finite QBD process

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Backpropagation-Friendly Eigendecomposition