In the present paper, we propose a new method for solving large-scale generalized differential Sylvester equations, by projecting the initial problem onto the extended block Krylov subspace with an orthogonality Galerkin condition. This projection gives rise to a low-dimensional generalized differential Sylvester matrix equation. The low-dimensional equations is then solved by Rosenbrock or BDF method. We give some theoretical results and report some numerical experiments to show the effectiveness of the proposed method.
Sadek, L. and Talibi Alaoui, H. (2020). The extended block Arnoldi method for solving generalized differential Sylvester equations. Journal of Mathematical Modeling, 8(2), 189-206. doi: 10.22124/jmm.2020.15871.1388
MLA
Sadek, L. , and Talibi Alaoui, H. . "The extended block Arnoldi method for solving generalized differential Sylvester equations", Journal of Mathematical Modeling, 8, 2, 2020, 189-206. doi: 10.22124/jmm.2020.15871.1388
HARVARD
Sadek, L., Talibi Alaoui, H. (2020). 'The extended block Arnoldi method for solving generalized differential Sylvester equations', Journal of Mathematical Modeling, 8(2), pp. 189-206. doi: 10.22124/jmm.2020.15871.1388
CHICAGO
L. Sadek and H. Talibi Alaoui, "The extended block Arnoldi method for solving generalized differential Sylvester equations," Journal of Mathematical Modeling, 8 2 (2020): 189-206, doi: 10.22124/jmm.2020.15871.1388
VANCOUVER
Sadek, L., Talibi Alaoui, H. The extended block Arnoldi method for solving generalized differential Sylvester equations. Journal of Mathematical Modeling, 2020; 8(2): 189-206. doi: 10.22124/jmm.2020.15871.1388
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