It is well-known that the symplectic Lanczos method is an efficient tool for computing a few eigenvalues of large and sparse Hamiltonian matrices. A variety of block Krylov subspace methods were introduced by Lopez and Simoncini to compute an approximation of $\exp(M)V$ for a given large square Hamiltonian matrix $M$ and a tall and skinny matrix $V$ that preserves the geometric property of $V$. For the same purpose, in this paper, we have proposed a new method based on a global version of the symplectic Lanczos algorithm, called the global $J$-Lanczos method ($GJ$-Lanczos). To the best of our knowledge, this is probably the first adaptation of the symplectic Lanczos method in the global case. Numerical examples are given to illustrate the effectiveness of the proposed approach.
Archid, A., & Bentbib, A. (2022). Global symplectic Lanczos method with application to matrix exponential approximation. Journal of Mathematical Modeling, 10(1), 143-160. doi: 10.22124/jmm.2021.19045.1631
MLA
Atika Archid; Abdeslem Hafid Bentbib. "Global symplectic Lanczos method with application to matrix exponential approximation". Journal of Mathematical Modeling, 10, 1, 2022, 143-160. doi: 10.22124/jmm.2021.19045.1631
HARVARD
Archid, A., Bentbib, A. (2022). 'Global symplectic Lanczos method with application to matrix exponential approximation', Journal of Mathematical Modeling, 10(1), pp. 143-160. doi: 10.22124/jmm.2021.19045.1631
VANCOUVER
Archid, A., Bentbib, A. Global symplectic Lanczos method with application to matrix exponential approximation. Journal of Mathematical Modeling, 2022; 10(1): 143-160. doi: 10.22124/jmm.2021.19045.1631
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