Solving rank-structured Sylvester and Lyapunov equations
We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium
and large scale, in case of rank-structured data, ie, when the coefficient matrices and the …
and large scale, in case of rank-structured data, ie, when the coefficient matrices and the …
Low-rank updates and a divide-and-conquer method for linear matrix equations
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 …
role in various applications, including the stability analysis and dimensionality reduction of …
On the convergence of Krylov methods with low-rank truncations
D Palitta, P Kürschner - Numerical Algorithms, 2021 - Springer
Low-rank Krylov methods are one of the few options available in the literature to address the
numerical solution of large-scale general linear matrix equations. These routines amount to …
numerical solution of large-scale general linear matrix equations. These routines amount to …
An improved complex-valued recurrent neural network model for time-varying complex-valued Sylvester equation
L Ding, L Xiao, K Zhou, Y Lan, Y Zhang, J Li - IEEE Access, 2019 - ieeexplore.ieee.org
Complex-valued time-varying Sylvester equation (CVTVSE) has been successfully applied
into mathematics and control domain. However, the computation load of solving CVTVSE …
into mathematics and control domain. However, the computation load of solving CVTVSE …
NEP-PACK: A Julia package for nonlinear eigenproblems-v0. 2
E Jarlebring, M Bennedich, G Mele, E Ringh… - arXiv preprint arXiv …, 2018 - arxiv.org
We present NEP-PACK a novel open-source library for the solution of nonlinear eigenvalue
problems (NEPs). The package provides a framework to represent NEPs, as well as efficient …
problems (NEPs). The package provides a framework to represent NEPs, as well as efficient …
Krylov methods for low‐rank commuting generalized Sylvester equations
E Jarlebring, G Mele, D Palitta… - Numerical Linear Algebra …, 2018 - Wiley Online Library
We consider generalizations of the Sylvester matrix equation, consisting of the sum of a
Sylvester operator and a linear operator Π with a particular structure. More precisely, the …
Sylvester operator and a linear operator Π with a particular structure. More precisely, the …
The Sherman–Morrison–Woodbury formula for generalized linear matrix equations and applications
Y Hao, V Simoncini - Numerical linear algebra with applications, 2021 - Wiley Online Library
We discuss the use of a matrix‐oriented approach for numerically solving the dense matrix
equation AX+ XA T+ M 1 XN 1+…+ M ℓ XN ℓ= F, with ℓ≥ 1, and M i, N i, i= 1,…, ℓ of low …
equation AX+ XA T+ M 1 XN 1+…+ M ℓ XN ℓ= F, with ℓ≥ 1, and M i, N i, i= 1,…, ℓ of low …
[HTML][HTML] Numerical solution of a class of quasi-linear matrix equations
M Porcelli, V Simoncini - Linear Algebra and its Applications, 2023 - Elsevier
Given the matrix equation A X+ X B+ f (X) C= D in the unknown n× m matrix X, we analyze
existence and uniqueness conditions, together with computational solution strategies for f: R …
existence and uniqueness conditions, together with computational solution strategies for f: R …
Preconditioning techniques for generalized Sylvester matrix equations
Y Voet - arXiv preprint arXiv:2307.07884, 2023 - arxiv.org
Sylvester matrix equations are ubiquitous in scientific computing. However, few solution
techniques exist for their generalized multiterm version, as they recently arose in stochastic …
techniques exist for their generalized multiterm version, as they recently arose in stochastic …
Greedy low-rank algorithm for spatial connectome regression
Recovering brain connectivity from tract tracing data is an important computational problem
in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as …
in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as …