The nonsymmetric Lanczos algorithm and controllability

DOI10.1016/0167-6911(91)90003-WzbMath0732.93004OpenAlexW4243877627MaRDI QIDQ809937

Gene H. Golub, Daniel L. Boley

Publication date: 1991

Published in: Systems \& Control Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-6911(91)90003-w

zbMATH Keywords

Lanczos algorithmlarge sparse systemsObservable spaceReachable Space

Mathematics Subject Classification ID

Related Items (12)

A rational Lanczos algorithm for model reduction ⋮ Adaptive rational interpolation: Arnoldi and Lanczos-like equations ⋮ A Krylov subspace projection method for simultaneous solution of Helmholtz problems at multiple frequencies. ⋮ Direct block tridiagonalization of single-input single-output systems ⋮ Reduction of large-scale dynamical systems by the Krylov subspaces method: analysis of approaches ⋮ The Lanczos algorithm and Hankel matrix factorization ⋮ A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms ⋮ Krylov space methods on state-space control models ⋮ Efficent computation of eigenvalues of randomly generated matrices ⋮ On the construction of real non-selfadjoint tridiagonal matrices with prescribed three spectra ⋮ Deflation in Krylov subspace methods and distance to uncontrollability ⋮ A Lanczos-type method for multiple starting vectors

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• The Lanczos-Arnoldi algorithm and controllability
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• Eigenvalues of perturbed Hermitian matrices
• Computing the Kalman decomposition: An optimal method
• A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
• On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
• Reduction to Tridiagonal Form and Minimal Realizations
• Controllability and Observability in Multivariable Control Systems
• Mathematical Description of Linear Dynamical Systems
• Estimates for Some Computational Techniques in Linear Algebra

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