Transpose-free multiple Lanczos and its application in Padé approximation

DOI10.1016/j.cam.2004.09.011zbMath1062.65046OpenAlexW2093281757MaRDI QIDQ1763763

Man-Chung Yeung, Daniel L. Boley

Publication date: 22 February 2005

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.09.011

zbMATH Keywords

numerical examplesPadé approximationKrylov subspace methodlinear dynamical systemModel reductionMPVL methodTFMPVL methodTranspose-free Lanczos method

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical optimization and variational techniques (65K10) Discrete-time control/observation systems (93C55) Iterative numerical methods for linear systems (65F10)

Related Items (2)

ML(\(n\))BiCGStabt: a ML(\(n\))BiCGStab variant with \(\mathbf A\)-transpose ⋮ A block IDR\((s)\) method for nonsymmetric linear systems with multiple right-hand sides

Uses Software

• SLICOT
• CGS

Cites Work

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• The Lanczos-Arnoldi algorithm and controllability
• Transpose-free formulations of Lanczos-type methods for nonsymmetric linear systems
• Error estimation on the Padé approximation of transfer functions via the Lanczos process
• BiCGstab(\(l\)) for linear equations involving unsymmetric matrices with complex spectrum
• Krylov space methods on state-space control models
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Reduction to Tridiagonal Form and Minimal Realizations
• Variants of BICGSTAB for Matrices with Complex Spectrum
• A Lanczos-type method for multiple starting vectors
• ML(k)BiCGSTAB: A BiCGSTAB Variant Based on Multiple Lanczos Starting Vectors
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
• Computation of matrix-valued formally orthogonal polynomials and applications

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