A structure preserving approximation method for Hamiltonian exponential matrices. (English) Zbl 1246.65076
Summary: The approximation of exp\((A)V\) where \(A\) is a real matrix and \(V\) a rectangular matrix is the key ingredient of many exponential integrators for solving systems of ordinary differential equations. In this paper we give an appropriate structure preserving approximation method to exp\((A)V\) when \(A\) is a Hamiltonian or skew-Hamiltonian \(2n\)-by-\(2n\) real matrix. Our approach is based on Krylov subspace methods that preserve Hamiltonian or skew-Hamiltonian structure. In this regard we use a symplectic Lanczos algorithm to compute the desired approximation.
MSC:
| 65F60 | Numerical computation of matrix exponential and similar matrix functions |
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
Keywords:
Hamiltonian matrix; exponential matrix; orthogonal; symplectic; numerical examples; exponential integrators; Krylov subspace methods; symplectic Lanczos algorithmSoftware:
QMRPACKReferences:
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