On matrix differential equations and abstract FG algorithm
type: Item
instance of: scholarly article
title: On matrix differential equations and abstract FG algorithm
zbMATH Open document ID: 1042.34021
DOI: 10.1016/S0024-3795(01)00511-0
author: Maria Przybylska
published in: Linear Algebra and its Applications
publication date: 2002-06-24T00:00:00Z
review text: The purpose of this paper is to show that a whole class of matrix differential equations has a connection with the abstract FG algorithm. All equations from this class are built by means of various representations \(\rho\) of an arbitrary Lie algebra \({\mathfrak g}\) on \(\mathbb{K}^{n\times n}\) in the following way: \[ \dot L=\rho_N(L) \] where \(L\in\mathbb{K}^{n\times n}\), and \(N=N(t,L)\in{\mathfrak g}\). Here the author assumes that \({\mathfrak g}\) is the Lie algebra of a certain closed subgroup \({\mathfrak h}\) of \(GL(n,\mathbb{K})\).
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 37J35
zbMATH DE Number: 1758613
zbMATH Keywords: isospectral flows
zbMATH Keywords: matrix differential equations
zbMATH Keywords: abstract FG algorithm
zbMATH Keywords: representations
zbMATH Keywords: Lie algebra
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Q3784460
cites work: Generalized Lax pairs, the modified classical Yang-Baxter equation, and affine geometry of Lie groups
cites work: Isospectral Flows and Abstract Matrix Factorizations
cites work: Q4315443
cites work: Ordinary Differential Equations and the Symmetric Eigenvalue Problem
cites work: The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
cites work: Numerical linear algorithms and group theory
cites work: Singular-value decomposition via gradient and self-equivalent flows
cites work: Q4255531
cites work: Integrals of nonlinear equations of evolution and solitary waves
cites work: Differential Equations and the $QR$ Algorithm
cites work: A new look at the Lanczos algorithm for solving symmetric systems of linear equations
cites work: A generalization of the Lax equation defined by an arbitrary anti-automorphism
cites work: A generalization of the Lax equation
cites work: A new integrable case of the motion of the 4-dimensional rigid body
cites work: Q5735511
cites work: What is a classical r-matrix?
cites work: Dressing transformations and Poisson group actions
cites work: The QR algorithm and scattering for the finite nonperiodic Toda lattice
cites work: Understanding the $QR$ Algorithm
cites work: Isospectral Flows
cites work: Self-similar flows
cites work: Self-Equivalent Flows Associated Decomposition
cites work: On Rutishauser’s Approach to Self-Similar Flows
cites work: Convergence of algorithms of decomposition type for the eigenvalue problem
cites work: Q5674306
description: scientific article; zbMATH DE number 1758613