A structure preserving approximation method for Hamiltonian exponential matrices

DOI10.1016/j.apnum.2011.03.006zbMath1246.65076OpenAlexW1981539758MaRDI QIDQ436000

A. Kanber, Said Agoujil, Abdeslem Hafid Bentbib

Publication date: 13 July 2012

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.03.006

zbMATH Keywords

numerical examplesKrylov subspace methodsHamiltonian matrixorthogonalsymplecticexponential integratorsexponential matrixsymplectic Lanczos algorithm

Mathematics Subject Classification ID

Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Numerical computation of matrix exponential and similar matrix functions (65F60)

Related Items (4)

An iterative method for computing a symplectic SVD-like decomposition ⋮ Approximation of the matrix exponential operator by a structure-preserving block Arnoldi-type method ⋮ Kolmogoroff-Nagumo mean over the affine symplectic group of matrices ⋮ Krylov projection methods for linear Hamiltonian systems

Uses Software

• QMRPACK

Cites Work

• Preserving geometric properties of the exponential matrix by block Krylov subspace methods
• A Krylov projection method for systems of ODEs
• Orthosymplectic integration of linear Hamiltonian systems
• The shift-inverted \(J\)-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations
• An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
• Krylov integrators for Hamiltonian systems
• Software for simplified Lanczos and QMR algorithms
• Methods for the approximation of the matrix exponential in a Lie-algebraic setting
• Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
• The Geometry of Algorithms with Orthogonality Constraints
• On Krylov Subspace Approximations to the Matrix Exponential Operator
• Computation of the Exponential of Large Sparse Skew-Symmetric Matrices
• Efficient Computation of the Matrix Exponential by Generalized Polar Decompositions
• The principle of minimized iterations in the solution of the matrix eigenvalue problem
• Computing Lyapunov exponents on a Stiefel manifold
• Unnamed Item

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