相关论文: Efficient solution of sequences of parametrized Ly…
A delay Lyapunov matrix corresponding to an exponentially stable system of linear time-invariant delay differential equations can be characterized as the solution of a boundary value problem involving a matrix valued delay differential…
We develop a mixed-precision iterative refinement framework for solving low-rank Lyapunov matrix equations $AX + XA^T + W =0$, where $W=LL^T$ or $W=LSL^T$. Via rounding error analysis of the algorithms we derive sufficient conditions for…
In the numerical treatment of large-scale Sylvester and Lyapunov equations, projection methods require solving a reduced problem to check convergence. As the approximation space expands, this solution takes an increasing portion of the…
In the present paper, we consider large-scale differential Lyapunov matrix equations having a low rank constant term. We present two new approaches for the numerical resolution of such differential matrix equations. The first approach is…
In this work, we propose a reduced basis method for efficient solution of parametric linear systems. The coefficient matrix is assumed to be a linear matrix-valued function that is symmetric and positive definite for admissible values of…
An efficient Krylov subspace algorithm for computing actions of the $\varphi$ matrix function for large matrices is proposed. This matrix function is widely used in exponential time integration, Markov chains and network analysis and many…
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,…
The numerical solution of large-scale Lyapunov matrix equations with symmetric banded data has so far received little attention in the rich literature on Lyapunov equations. We aim to contribute to this open problem by introducing two…
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…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction. The few available…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…
The numerical integration of stiff equations is a challenging problem that needs to be approached by specialized numerical methods. Exponential integrators form a popular class of such methods since they are provably robust to stiffness and…
In the present paper, we propose Krylov-based methods for solving large-scale differential Sylvester matrix equations having a low rank constant term. We present two new approaches for solving such differential matrix equations. The first…
We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…
This survey explores modern approaches for computing low-rank approximations of high-dimensional matrices by means of the randomized SVD, randomized subspace iteration, and randomized block Krylov iteration. The paper compares the…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
One of the most computationally expensive steps of the low-rank ADI method for large-scale Lyapunov equations is the solution of a shifted linear system at each iteration. We propose the use of the extended Krylov subspace method for this…