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An Implicitly Symplectic Lanczos Algorithm for Hamiltonian Matrices

S. Agoujil, A.H. Bentbib

Abstract


The purpose of this paper is to outline a structure-preserving Lanczos-type algorithm, named implicitly symplectic Lanczos algorithm for real Hamiltonian matrices. The algorithm is based on a symplectic reduction procedure of Hamiltonian matrix using symplectic similarity transformations with symplectic reflectors defined on R2n×2. Numerical results for the proposed algorithm are treated.

Keywords


Krylov subspace, Hamiltonian, Skew-Hamiltonian and symplectic matrices, symplectic reflector, Symplectic Arnoldi, J-Hessenberg form, Symplectic Lanczos.

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