A structure preserving flow for computing Hamiltonian matrix exponential

Yueh Cheng Kuo; Wen Wei Lin; Shih Feng Shieh

doi:10.1007/s00211-019-01065-3

A structure preserving flow for computing Hamiltonian matrix exponential

Yueh Cheng Kuo^*
, Wen Wei Lin
, Shih Feng Shieh

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

This article focuses on computing Hamiltonian matrix exponential. Given a Hamiltonian matrix H, it is well-known that the matrix exponential e^H is a symplectic matrix and its eigenvalues form reciprocal (λ, 1 / λ¯ ). It is important to take care of the symplectic structure for computing e^H. Based on the structure-preserving flow proposed by Kuo et al. (SIAM J Matrix Anal Appl 37:976–1001, 2016), we develop a numerical method for computing the symplectic matrix pair (M, L) which represents e^H.

Original language	English
Pages (from-to)	555-582
Number of pages	28
Journal	Numerische Mathematik
Volume	143
Issue number	3
DOIs	https://doi.org/10.1007/s00211-019-01065-3
Publication status	Published - 2019 Nov 1

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1007/s00211-019-01065-3

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abstract = "This article focuses on computing Hamiltonian matrix exponential. Given a Hamiltonian matrix H, it is well-known that the matrix exponential eH is a symplectic matrix and its eigenvalues form reciprocal (λ, 1 / λ¯ ). It is important to take care of the symplectic structure for computing eH. Based on the structure-preserving flow proposed by Kuo et al. (SIAM J Matrix Anal Appl 37:976–1001, 2016), we develop a numerical method for computing the symplectic matrix pair (M, L) which represents eH.",

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AU - Lin, Wen Wei

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N2 - This article focuses on computing Hamiltonian matrix exponential. Given a Hamiltonian matrix H, it is well-known that the matrix exponential eH is a symplectic matrix and its eigenvalues form reciprocal (λ, 1 / λ¯ ). It is important to take care of the symplectic structure for computing eH. Based on the structure-preserving flow proposed by Kuo et al. (SIAM J Matrix Anal Appl 37:976–1001, 2016), we develop a numerical method for computing the symplectic matrix pair (M, L) which represents eH.

AB - This article focuses on computing Hamiltonian matrix exponential. Given a Hamiltonian matrix H, it is well-known that the matrix exponential eH is a symplectic matrix and its eigenvalues form reciprocal (λ, 1 / λ¯ ). It is important to take care of the symplectic structure for computing eH. Based on the structure-preserving flow proposed by Kuo et al. (SIAM J Matrix Anal Appl 37:976–1001, 2016), we develop a numerical method for computing the symplectic matrix pair (M, L) which represents eH.

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A structure preserving flow for computing Hamiltonian matrix exponential

Abstract

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