Structure-preserving Krylov Subspace Approximations for the Matrix Exponential of Hamiltonian Matrices: A Comparative Study
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914342246547456 |
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| author | Benner, Peter Faßbender, Heike Senn, Michel-Niklas |
| author_facet | Benner, Peter Faßbender, Heike Senn, Michel-Niklas |
| contents | We study structure-preserving Krylov subspace methods for approximating the matrix-vector products f(H)b, where H is a large Hamiltonian matrix and f denotes either the matrix exponential or the related phi-function. Such computations are central to exponential integrators for Hamiltonian systems. Standard Krylov methods generally destroy the Hamiltonian structure under projection, motivating the use of Krylov bases with J-orthogonal columns that yield Hamiltonian projected matrices and symplectic reduced exponentials. We compare several such structure-preserving Krylov methods on representative Hamiltonian test problems, focusing on accuracy, efficiency, and structure preservation, and briefly discuss adaptive strategies for selecting the Krylov subspace dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_18937 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structure-preserving Krylov Subspace Approximations for the Matrix Exponential of Hamiltonian Matrices: A Comparative Study Benner, Peter Faßbender, Heike Senn, Michel-Niklas Numerical Analysis 15A15, 65F55, 65F60 We study structure-preserving Krylov subspace methods for approximating the matrix-vector products f(H)b, where H is a large Hamiltonian matrix and f denotes either the matrix exponential or the related phi-function. Such computations are central to exponential integrators for Hamiltonian systems. Standard Krylov methods generally destroy the Hamiltonian structure under projection, motivating the use of Krylov bases with J-orthogonal columns that yield Hamiltonian projected matrices and symplectic reduced exponentials. We compare several such structure-preserving Krylov methods on representative Hamiltonian test problems, focusing on accuracy, efficiency, and structure preservation, and briefly discuss adaptive strategies for selecting the Krylov subspace dimension. |
| title | Structure-preserving Krylov Subspace Approximations for the Matrix Exponential of Hamiltonian Matrices: A Comparative Study |
| topic | Numerical Analysis 15A15, 65F55, 65F60 |
| url | https://arxiv.org/abs/2602.18937 |