Atika Archid,
Abdeslem Hafid Bentbib,
Said Agoujil
S. 26 - 42
doi:
10.1553/etna_vol52s26
Verlag der Österreichischen Akademie der Wissenschaften
doi:
10.1553/etna_vol52s26
Abstract:
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.
block J-Lanczos method, Hamiltonian matrix, skew-Hamiltonian matrix, symplectic matrix, symplectic reflector, block J-tridiagonal form, block J-Hessenberg form
Published Online:
2020/01/28 10:03:09
Object Identifier:
0xc1aa5576 0x003b3d12
Rights:All rights reserved.For questions regarding copyright and copies please contact us by email.
Electronic Transactions on Numerical Analysis (ETNA) is an electronic journal for the publication of significant new developments in numerical analysis and scientific computing. Papers of the highest quality that deal with the analysis of algorithms for the solution of continuous models and numerical linear algebra are appropriate for ETNA, as are papers of similar quality that discuss implementation and performance of such algorithms. New algorithms for current or new computer architectures are appropriate provided that they are numerically sound. However, the focus of the publication should be on the algorithm rather than on the architecture. The journal is published by the Kent State University Library in conjunction with the Institute of Computational Mathematics at Kent State University, and in cooperation with the Johann Radon Institute for Computational and Applied Mathematics of the Austrian Academy of Sciences (RICAM). Reviews of all ETNA papers appear in Mathematical Reviews and Zentralblatt für Mathematik. Reference information for ETNA papers also appears in the expanded Science Citation Index. ETNA is registered with the Library of Congress and has ISSN 1068-9613.
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