Error analysis of symplectic Lanczos method for Hamiltonian eigenvalue problem

DOI10.1007/s11464-006-0017-7zbMath1222.65036OpenAlexW1878894416MaRDI QIDQ719952

Qingyou Yan, Xiaopeng Wei

Publication date: 12 October 2011

Published in: Frontiers of Mathematics in China (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11464-006-0017-7

zbMATH Keywords

eigenvalueerror analysisHamiltonian matrixRitz vectorRitz valuesymplectic Lanczos method

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Cites Work

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• Solution of the large matrix equations which occur in response theory
• An implicitly restarted symplectic Lanczos method for the Hamiltonian eigenvalue problem
• A numerically stable, structure preserving method for computing the eigenvalues of real Hamiltonian or symplectic pencils
• Error analysis of the symplectic Lanczos method for the symplectic eigenvalue problem
• Residual Bounds on Approximate Eigensystems of Nonnormal Matrices
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Error Analysis of the Lanczos Algorithm for the Nonsymmetric Eigenvalue Problem
• A symplectic QR like algorithm for the solution of the real algebraic Riccati equation

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