A BLOCK J-LANCZOS METHOD FOR HAMILTONIAN MATRICES

被引:1
|
作者
Archid, Atika [1 ]
Bentbib, Abdeslem Hafid [2 ]
Agoujil, Said [3 ]
机构
[1] Ibn Zohr Univ, Fac Sci, Lab LabSI, Agadir, Morocco
[2] Cadi Ayyad Univ, Fac Sci & Technol, Lab LAMAI, Marrakech, Morocco
[3] Moulay Ismail Univ, Fac Sci & Technol, Errachidia, Morocco
来源
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2020年 / 52卷
关键词
block J-Lanczos method; Hamiltonian matrix; skew-Hamiltonian matrix; symplectic matrix; symplectic reflector; block J-tridiagonal form; block J-Hessenberg form; KRYLOV SUBSPACE APPROXIMATIONS; INTEGRATORS; ALGORITHM;
D O I
10.1553/etna_vol52s26
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
This work aims to present a structure-preserving block Lanczos-like method. The Lanczos-like algorithm is an effective way to solve large sparse Hamiltonian eigenvalue problems. It can also be used to approximate exp(A) V for a given large square matrix A and a tall-and-skinny matrix V such that the geometric property of V is preserved, which interests us in this paper. This approximation is important for solving systems of ordinary differential equations (ODEs) or time-dependent partial differential equations (PDEs). Our approach is based on a block J-tridiagonalization procedure of a Hamiltonian and skew-symmetric matrix using symplectic similarity transformations.
引用
收藏
页码:26 / 42
页数:17
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