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Concept

Matrix differential equation

Related publications (16)

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Simone Deparis, Riccardo Tenderini

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 ...

Siam Publications2024

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 ...

SPRINGER2023

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

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, Wei Wang, Yinlin Hu, Zheng Dang

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

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

Alfio Quarteroni, Niccolò Dal Santo

The aim of this work is to propose and analyse a new high-order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second-order ordinary differential equations. These equations typically arise after space semidisc ...

OXFORD UNIV PRESS2018

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Petar Sirkovic

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

EPFL2016

Truncated low-rank methods for solving general linear matrix equations

Daniel Kressner, Petar Sirkovic

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

Bivariate Matrix Functions

Daniel Kressner

A definition of bivariate matrix functions is introduced and some theoretical as well as algorithmic aspects are analyzed. It is shown that our framework naturally extends the usual notion of (univariate) matrix functions and allows to unify existing resul ...

Element2014

Contribution to Integral Equation Techniques for Solving Electromagnetic Problems

Sergio Lopez Pena

Surface Mixed Potential Integral Equation (MPIE) formulations together with the Method of Moments (MoM) are widely used to solve electromagnetic problems. An accurate evaluation of the Green functions (GF) associated to the integral equation and of the cou ...

EPFL2010

BECOOL: Ballooning eigensolver with COOL finite elements

Jonathan Graves, Wilfred Anthony Cooper

An incompressible variational ideal ballooning mode equation is discretized with the COOL finite element discretization scheme using basis functions composed of variable order Legendre polynomials. This reduces the second order ordinary differential equati ...

2009

Unified formulation for Reissner-Mindlin plates: a comparison with numerical results

Luca Tassinari

Analytical solutions to problems of solids mechanics are useful to test the accuracy and the precision of the numerical approaches. Problems such as shear locking or boundary layer can be better understood with the help of analytical solutions. However, it ...

IASS Symposium 2009, Valencia, Spain2009

Singularly perturbed piecewise deterministic games

In this paper we consider a class of hybrid stochastic games with the piecewise open-loop information structure. These games are indexed over a parameter