On Hamiltonian and symplectic Lanczos processes
The author examines the relationship between various structure-preserving Krylov subspace methods for computing partial eigensystems of large sparse skew-Hamiltonian, Hamiltonian and symplectic matrices. Parameters in families of implicitly restarted Lanczos methods, proposed by \textit{P. Benner} and \textit{H. Fassbender} [ibid. 263, 75--111 (1987; Zbl 0884.65028); SIAM J. Matrix Anal. Appl. 22, No.~3, 682--713 (2000; Zbl 0985.65026)], are selected to condense the process as much as possible. The condensed Hamiltonian Lanczos process applied to the Hamiltonian matrix \(H\) is shown to be equivalent to the unsymmetric Lanczos process applied to the skew-Hamiltonian matrix \(H^2\) but to require roughly half as much computation. The condensed symplectic Lanczos process applied to a symplectic matrix \(S\) is shown to be equivalent to the unsymmetric Lanczos process applied to \(S+S^{-1}\) and to require roughly half as much computation.
scientific article; zbMATH DE number 2083505