University of Guilan Journal of Mathematical Modeling 2345-394X 10 1 2022 01 01 Global symplectic Lanczos method with application to matrix exponential approximation 143 160 4915 10.22124/jmm.2021.19045.1631 EN Atika Archid Laboratory LabSI, Faculty of Science, University Ibn Zohr, Agadir Abdeslem Hafid Bentbib Laboratory LAMAI, Faculty of Science and Technology, University Cadi Ayyad, Marrakesh Journal Article 2021 03 14 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. https://jmm.guilan.ac.ir/article_4915_20631a0918e8c42194c8307d50df6b5d.pdf