Applications of the Cayley approach in the numerical solution of matrix differential systems on quadratic groups

DOI10.1016/S0168-9274(99)00049-5zbMath0981.65080OpenAlexW2081625284MaRDI QIDQ1596331

Tiziano Politi, Luciano Lopez

Publication date: 1 April 2002

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(99)00049-5

zbMATH Keywords

numerical examplesLyapunov exponentsStiefel manifoldHamiltonian systemsconservative methodsLorentz groupmatrix differential systemsHamiltonian isospectral problemsPenrose regression problemquadratic groups

Mathematics Subject Classification ID

Geometric methods in ordinary differential equations (34A26) Linear ordinary differential equations and systems (34A30) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items

Geometric integration on Lie groups using the Cayley transform with focus on lattice QCD, On the Floquet-Magnus expansion: applications in solid-state nuclear magnetic resonance and physics, Numerical methods for ordinary differential equations on matrix manifolds, Piecewise interpolants on matrix Lie groups, Dynamical reduced basis methods for Hamiltonian systems, Topics in structure-preserving discretization

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• One step semi-explicit methods based on the Cayley transform for solving isospectral flows
• The Cayley transform in the numerical solution of unitary differential systems
• Runge-Kutta methods adapted to manifolds and based on rigid frames
• On the implementation of the method of Magnus series for linear differential equations
• On real logarithms of nearby matrices and structured matrix interpolation
• Numerical integration of ordinary differential equations on manifolds
• Conserving algorithms for the dynamics of Hamiltonian systems on Lie groups
• Orthosymplectic integration of linear Hamiltonian systems
• Structure of dynamical systems. A symplectic view of physics. Transl. from the French by C. H. Cushman-de Vries. Transl. ed.: R. H. Cushman a. G. M. Tuynman
• Numerical procedures based on Runge-Kutta methods for solving isospectral flows
• Runge-Kutta methods on Lie groups
• Computation of a few Lyapunov exponents for continuous and discrete dynamical systems
• Isospectral Flows and Abstract Matrix Factorizations
• On the solution of linear differential equations in Lie groups
• Collocation and Relaxed Collocation for the Fer and the Magnus Expansions
• Unitary Integrators and Applications to Continuous Orthonormalization Techniques
• Numerical solution of isospectral flows
• Solving ODEs numerically while preserving a first integral
• Runge-Kutta methods for orthogonal and isospectral flows
• Runge-Kutta type methods for orthogonal integration