From su(2) Gaudin Models to Integrable Tops [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2007 In the present paper we derive two well-known integrable cases of rigid body dynamics (the Lagrange top and the Clebsch system) performing an algebraic contraction on the two-body Lax matrices governing the (classical) su(2) Gaudin models.
Matteo Petrera, Orlando Ragnisco
doaj +8 more sources
Algebraic systems of matrices and Gröbner basis theory
Linear Algebra and its Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
G. Bourgeois
openaire +2 more sources
Algebraic properties of Manin matrices II: q-analogues and integrable systems [PDF]
Advances in Applied Mathematics, 2012 We study a natural q-analogue of a class of matrices with noncommutative entries, which were first considered by Yu. I. Manin in 1988 in relation with quantum group theory, (called Manin Matrices in [5]) .
Chervov, A. +3 more
core +3 more sources
Modification Methods for Inverting Matrices and Solving Systems of Linear Algebraic Equations [PDF]
Mathematics of Computation, 1972 Modification methods for inverting matrices and solving systems of linear algebraic equations are developed from Broyden’s rank-one modification formula. Several algorithms are presented that take as few, or nearly as few, arithmetic operations as Gaussian elimination and are well suited for the handling of data.
D. Goldfarb
openaire +3 more sources
Block-encoding dense and full-rank kernels using hierarchical matrices: applications in quantum numerical linear algebra [PDF]
Quantum, 2022 Many quantum algorithms for numerical linear algebra assume black-box access to a block-encoding of the matrix of interest, which is a strong assumption when the matrix is not sparse.
Quynh T. Nguyen +2 more
doaj +3 more sources
On equivalence of algebraic and finite element formulations of prestressed bar structures [PDF]
Scientific ReportsThe equivalence of the finite element method and the algebraic formulation of the equations of moderately thick and thin elastic frames, beams, trusses, and grillages within the Timoshenko and Euler-Bernoullie theory derived earlier by Pełczyński ...
Jan Pełczyński
doaj +2 more sources
Explicit preconditioning of systems of linear algebraic equations with dense matrices
Journal of Soviet Mathematics, 1988 For linear systems of equations \(Ax=b\) with full nonsymmetric nondiagonal dominant matrix of great order an explicit preconditioning G for the best convergence of an iterative method, in this case ORTHOMIN(k), is suggested. The structure of the preconditioning matrix G depends on the module of the elements of the matrix A. Three types of the strategy
L. Y. Kolotilina
openaire +4 more sources
Performance Analysis of Effective Symbolic Methods for Solving Band Matrix SLAEs [PDF]
EPJ Web of Conferences, 2019 This paper presents an experimental performance study of implementations of three symbolic algorithms for solving band matrix systems of linear algebraic equations with heptadiagonal, pentadiagonal, and tridiagonal coefficient matrices.
Veneva Milena, Ayriyan Alexander
doaj +4 more sources
Algebraic and Geometric Aspects of Integrable Systems and Random Matrices [PDF]
, 2013 A. Dzhamay, K. Maruno, V. Pierce
openaire +2 more sources
The dual fuzzy matrix equations: Extended solution, algebraic solution and solution
AIMS Mathematics, 2023 In this paper, we propose a direct method to solve the dual fuzzy matrix equation of the form $ \mathbf{A}\widetilde{\mathbf{X}}+\widetilde{\mathbf{B}} = \mathbf{C}\widetilde{\mathbf{X}}+\widetilde{\mathbf{D}} $ with $ \mathbf{A} $, $ \mathbf{C ...
Zengtai Gong , Jun Wu, Kun Liu
doaj +1 more source