The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method

DOI10.1016/S0024-3795(97)10049-0zbMath0935.65030OpenAlexW2055566907WikidataQ127360650 ScholiaQ127360650MaRDI QIDQ1307194

Peter Benner, Heike Fassbender

Publication date: 28 October 1999

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0024-3795(97)10049-0

zbMATH Keywords

reductionsymplectic matricessymplectic Lanczos methodSR algorithmsymplectic butterfly formsymplectic eigenvalue problem

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (16)

Two connections between the \(SR\) and \(HR\) eigenvalue algorithms ⋮ Fifty Three Matrix Factorizations: A Systematic Approach ⋮ First order structure-preserving perturbation theory for eigenvalues of symplectic matrices. II ⋮ A collection of efficient retractions for the symplectic Stiefel manifold ⋮ First Order Structure-Preserving Perturbation Theory for Eigenvalues of Symplectic Matrices ⋮ Backward Error Analysis for Eigenproblems Involving Conjugate Symplectic Matrices ⋮ Laurent skew orthogonal polynomials and related symplectic matrices ⋮ Large-scale discrete-time algebraic Riccati equations -- doubling algorithm and error analysis ⋮ The parameterized 𝑆𝑅 algorithm for symplectic (butterfly) matrices ⋮ Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods ⋮ Krylov subspace methods for discrete-time algebraic Riccati equations ⋮ A block \(J\)-Lanczos method for Hamiltonian matrices ⋮ Large-scale algebraic Riccati equations with high-rank constant terms ⋮ On Hamiltonian and symplectic Lanczos processes ⋮ A Core-Chasing Symplectic QR Algorithm ⋮ \(SR\) and \(SZ\) algorithms for the symplectic (butterfly) eigenproblem

Uses Software

• eigs
• IRAM

Cites Work

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