A symplectic method for approximating all the eigenvalues of a Hamiltonian matrix
From MaRDI portal
Publication:1058816
DOI10.1016/0024-3795(84)90034-XzbMath0565.65018OpenAlexW2328218167MaRDI QIDQ1058816
Publication date: 1984
Published in: Linear Algebra and its Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0024-3795(84)90034-x
Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Eigenvalues, singular values, and eigenvectors (15A18) Hermitian, skew-Hermitian, and related matrices (15B57)
Related Items
A class of Hamiltonian-symplectic methods for solving the algebraic Riccati equation ⋮ A Structure Preserving Shift-Invert Infinite Arnoldi Algorithm for a Class of Delay Eigenvalue Problems with Hamiltonian Symmetry ⋮ Balancing sparse Hamiltonian eigenproblems ⋮ Properties of a quadratic matrix equation and the solution of the continuous-time algebraic Riccati equation ⋮ Rank-adaptive structure-preserving model order reduction of Hamiltonian systems ⋮ A new method for computing the closed-loop eigenvalues of a discrete-time algebraic Riccati equation ⋮ Hamiltonian partial mixed finite element-state space symplectic semi-analytical approach for the piezoelectric smart composites and FGM analysis ⋮ A numerical method for computing the Hamiltonian Schur form ⋮ The shift-inverted \(J\)-Lanczos algorithm for the numerical solutions of large sparse algebraic Riccati equations ⋮ An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem ⋮ A bisection method for computing the \(H_{\infty}\) norm of a transfer matrix and related problems ⋮ A new method for computing the stable invariant subspace of a real Hamiltonian matrix ⋮ Two connections between the \(SR\) and \(HR\) eigenvalue algorithms ⋮ Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method ⋮ Skew-symmetric matrix polynomials and their Smith forms ⋮ An economical algorithm for calculating the coneigenvalues of complex matrices that are self-adjoint with respect to the symplectic metric ⋮ An efficient and stable structure preserving algorithm for computing the eigenvalues of a Hamiltonian matrix ⋮ A collection of efficient retractions for the symplectic Stiefel manifold ⋮ Simultaneous Hollowization, Joint Numerical Range, and Stabilization by Noise ⋮ An upper \(J\)-Hessenberg reduction of a matrix through symplectic Householder transformations ⋮ A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its \(L_{\infty}\)-norm ⋮ Computation of threshold conditions for epidemiological models and global stability of the disease-free equilibrium (DFE) ⋮ Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms ⋮ Real fast structure-preserving algorithm for eigenproblem of complex Hermitian matrices ⋮ An exact symplectic geometry solution for the static and dynamic analysis of Reissner plates ⋮ Optimal symplectic Householder transformations for \(SR\) decomposition ⋮ A note on the stability of two-level symplectic schemes ⋮ Efficient and accurate algorithms for solving the Bethe-Salpeter eigenvalue problem for crystalline systems ⋮ A novel symmetric skew-Hamiltonian isotropic Lanczos algorithm for spectral conformal parameterizations ⋮ An open-source ABAQUS implementation of the scaled boundary finite element method to study interfacial problems using polyhedral meshes ⋮ Eigenvalue problem of a large scale indefinite gyroscopic dynamic system ⋮ On structured componentwise condition numbers for Hamiltonian eigenvalue problems ⋮ Self-adjoint differential-algebraic equations ⋮ Symplectic Householder transformations for a QR-like decomposition, a geometric and algebraic approaches ⋮ Hamilton and Jacobi come full circle: Jacobi algorithms for structured Hamiltonian eigenproblems ⋮ A structure-preserving method for positive realness problem in control ⋮ On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms ⋮ A hybrid symplectic principal component analysis and central tendency measure method for detection of determinism in noisy time series with application to mechanomyography ⋮ On a finite algorithm for computing neutral subspaces of skew-symmetric matrices ⋮ An algorithm for the computation of the structured complex stability radius ⋮ Structured Eigenvalue Problems ⋮ A global minimum search algorithm for estimating the distance to uncontrollability ⋮ On computing the eigenvalues of a symplectic pencil ⋮ The solution of weak formulation for axisymmetric problem of orthotropic cantilever cylindrical shell ⋮ On Hamiltonian and symplectic Hessenberg forms ⋮ A treatment of breakdowns and near breakdowns in a reduction of a matrix to upper \(J\)-Hessenberg form and related topics ⋮ Matrix factorizations for symplectic QR-like methods ⋮ On the product of two skew-Hamiltonian or two skew-symmetric matrices ⋮ Refined rigorous perturbation bounds for the SR decomposition ⋮ Detection of generic one parameter bifurcations of Hamiltonian equilibria ⋮ Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras ⋮ Hamiltonian square roots of skew-Hamiltonian matrices ⋮ A method of embedding dimension estimation based on symplectic geometry ⋮ Numerical methods in control ⋮ The symplectic eigenvalue problem, the butterfly form, the SR algorithm, and the Lanczos method ⋮ Numerical methods and questions in the organization of calculus. XII. Transl. from the Russian ⋮ Computing the CS and the generalized singular value decompositions ⋮ Computing Symplectic Eigenpairs of Symmetric Positive-Definite Matrices via Trace Minimization and Riemannian Optimization ⋮ The Moser-Veselov equation ⋮ The properties of a kind of random symplectic matrices ⋮ Symplectic factorizations and parallel iterative algorithms for tridiagonal systems of equations
Uses Software
Cites Work
