On theoretical and numerical aspects of symplectic Gram-Schmidt-like algorithms

DOI10.1007/s11075-005-0963-2zbMath1111.65038OpenAlexW1988819385MaRDI QIDQ2501237

Ahmed Salam

Publication date: 4 September 2006

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-005-0963-2

zbMATH Keywords

numerical experimentskew-symmetric scalar productsymplectic Gram-Schmidt algorithmlarge sparse Hamiltonian eigenvalue problems

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Orthogonalization in numerical linear algebra (65F25)

Related Items (15)

Reduced basis methods for time-dependent problems ⋮ The transfer function of generic linear quantum stochastic systems has a pure cascade realization ⋮ On the conditioning of factors in the SR decomposition ⋮ Rank-adaptive structure-preserving model order reduction of Hamiltonian systems ⋮ Preserving geometric properties of the exponential matrix by block Krylov subspace methods ⋮ Perturbation analysis for the symplectic QR factorization ⋮ Optimization on the symplectic Stiefel manifold: SR decomposition-based retraction and applications ⋮ Structure-preserving model order reduction of Hamiltonian systems ⋮ An upper \(J\)-Hessenberg reduction of a matrix through symplectic Householder transformations ⋮ Equivalence between modified symplectic Gram-Schmidt and Householder SR algorithms ⋮ On the strong stability of symplectic matrices ⋮ A spectral trichotomy method for symplectic matrices ⋮ Structure-preserving reduced basis methods for Poisson systems ⋮ Refined rigorous perturbation bounds for the SR decomposition ⋮ Gaussian distributions on Riemannian symmetric spaces in the large \(N\) limit

Uses Software

• QMRPACK
• mctoolbox

Cites Work

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