\(SR\) and \(SZ\) algorithms for the symplectic (butterfly) eigenproblem

DOI10.1016/S0024-3795(98)10090-3zbMath0947.65044MaRDI QIDQ1301293

David S. Watkins, Peter Benner, Heike Fassbender

Publication date: 14 February 2000

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

zbMATH Keywords

numerical exampleseigenvaluesconvergence accelerationeigenvectorssymplectic matrix\(SR\) algorithm\(J\)-orthogonal matrix\(SZ\) algorithmbutterfly matricessymplectic triangular factorization

Mathematics Subject Classification ID

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

Related Items (6)

A collection of efficient retractions for the symplectic Stiefel manifold ⋮ Laurent skew orthogonal polynomials and related symplectic matrices ⋮ On the numerical solution of large-scale sparse discrete-time Riccati equations ⋮ The parameterized 𝑆𝑅 algorithm for symplectic (butterfly) matrices ⋮ On Hamiltonian and symplectic Lanczos processes ⋮ A Core-Chasing Symplectic QR Algorithm

Uses Software

• LAPACK

Cites Work

• Convergence of algorithms of decomposition type for the eigenvalue problem
• A Schur decomposition for Hamiltonian matrices
• The weak and strong stability of algorithms in numerical linear algebra
• An analysis of the HR algorithm for computing the eigenvalues of a matrix
• Schur parameter pencils for the solution of the unitary eigenproblem
• The autonomous linear quadratic control problem. Theory and numerical solution
• Numerical linear algorithms and group theory
• On some algebraic problems in connection with general eigenvalue algorithms
• The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method
• Matrix factorizations for symplectic QR-like methods
• Linear Hamiltonian difference systems: Disconjugacy and Jacobi-type conditions
• The QR Transformation A Unitary Analogue to the LR Transformation--Part 1
• Chasing Algorithms for the Eigenvalue Problem
• On the numerical solution of the discrete-time algebraic Riccati equation
• Theory of Decomposition and Bulge-Chasing Algorithms for the Generalized Eigenvalue Problem
• A symplectic QR like algorithm for the solution of the real algebraic Riccati equation
• The Problem of Lateral Buckling of Cantilever Plates
• On some algorithms for the solution of the complete eigenvalue problem
• A Geometric Theory for the $QR$, $LU$ and Power Iterations
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