Applications of the Lanczos method

DOI10.1016/0010-4655(89)90157-4zbMath0798.65073OpenAlexW1986034826MaRDI QIDQ1330637

Bahram Nour-Omid

Publication date: 30 October 1994

Published in: Computer Physics Communications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0010-4655(89)90157-4

zbMATH Keywords

algorithmlinear systemsfeedback controlgeneralized eigenproblemLanczos vectorsdamped beam problemunsymmetric two sided Lanczos method

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Feedback control (93B52) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (9)

Solving structural mechanics problems on the CalTech hypercube machine ⋮ Lanczos algorithm for the quadratic eigenvalue problem in engineering applications ⋮ Rational approximation to the Fermi-Dirac function with applications in density functional theory ⋮ The infinite Lanczos method for symmetric nonlinear eigenvalue problems ⋮ APPROXIMATION OF THE LINEAR COMBINATION OF <i>φ</i>-FUNCTIONS USING THE BLOCK SHIFT-AND-INVERT KRYLOV SUBSPACE METHOD ⋮ A numerical algorithm for the diffusion equation using 3D FEM and the Arnoldi method ⋮ Block Krylov subspace methods for approximating the linear combination of \(\varphi\)-functions arising in exponential integrators ⋮ Approximation of matrix operators applied to multiple vectors ⋮ New methods for calculations of the lowest eigenvalues of the real symmetric generalized eigenvalue problem

Cites Work

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• The use of a refined error bound when updating eigenvalues of tridiagonals
• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• The Lanczos Algorithm With Partial Reorthogonalization
• Lanczos versus subspace iteration for solution of eigenvalue problems
• Lanczos method for heat conduction analysis
• How to Implement the Spectral Transformation
• The Lanczos Algorithm with Selective Orthogonalization
• Evaluation of orthogonal damping matrices
• The Calculation of Eigenvectors by the Method of Lanczos

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