High-order symplectic Lie group methods on \(SO(n)\) using the polar decomposition

DOI10.3934/jcd.2022003OpenAlexW4214743283MaRDI QIDQ2093490

Khoa Tran, Melvin Leok, Xuefeng Shen

Publication date: 8 November 2022

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2201.10768

zbMATH Keywords

symplectic integrationrotation grouppolar decompositionvariational integratorgeometric numerical integrationLie group integrator

Mathematics Subject Classification ID

General theory of numerical analysis in abstract spaces (65J05) Index theory and related fixed-point theorems on manifolds (58J20) Hamilton's principle (70H25) Numerical solutions to equations with linear operators (65J10) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Fixed-point iterations (47J26)

Cites Work

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• High-order symplectic partitioned Lie group methods
• Lie group spectral variational integrators
• General techniques for constructing variational integrators
• Lie group variational integrators for the full body problem in orbital mechanics
• Discrete mechanics and variational integrators
• A Hessenberg-Schur method for the problem AX + XB= C
• A variational perspective on accelerated methods in optimization
• Discrete Euler-Poincaré and Lie-Poisson equations
• A Class of Intrinsic Schemes for Orthogonal Integration
• Adaptive Hamiltonian Variational Integrators and Applications to Symplectic Accelerated Optimization
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]
• A Variational Formulation of Accelerated Optimization on Riemannian Manifolds
• Generalized polar decompositions on Lie groups with involutive automorphisms

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