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A rounding error analysis for the symplectic Lanczos method is given to solve the large-scale sparse Hamiltonian eigenvalue problem. If no breakdown occurs in the method, then it can be shown that the Hamiltonian structure preserving requirement does not destroy the essential feature of the nonsymmetric Lanczos algorithm. The relationship between the loss of J-orthogonality among the symplectic Lanczos vectors and the convergence of the Ritz values in the symmetric Lanczos algorithm is discussed. It is demonstrated that under certain assumptions the computed J-orthogonal Lanczos vectors lose the J-orthogonality when some Ritz values begin to converge. Our analysis closely follows the recent works of Bai and Fabbender.

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Synthesis and Design of Passive Runge-Kutta Methods

Fränken

Ochs

2001

AEU - International Journal of Electronics and Communications

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Cited by 6 publications

References 12 publications

Breaking Van Loan’s Curse: A Quest forStructure-Preserving Algorithms for Dense Structured Eigenvalue Problems

Breaking Van Loan’s Curse: A Quest forStructure-Preserving Algorithms for Dense Structured Eigenvalue Problems

Error analysis of symplectic Lanczos method for Hamiltonian eigenvalue problem

Synthesis and Design of Passive Runge-Kutta Methods

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