The Lanczos phenomenon - An interpretation based upon conjugate gradient optimization

DOI10.1016/0024-3795(80)90231-1zbMath0424.65009OpenAlexW1992787463MaRDI QIDQ1135080

Ralph A. Willoughby, Jane K. Cullum

Publication date: 1980

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0024-3795(80)90231-1

zbMATH Keywords

convergenceLanczos vectorsconjugate gradient optimization procedureLanczos eigenvalue proceduresLanczos tridiagonalization proceduresymmetric, positive definite matrix

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10) Orthogonalization in numerical linear algebra (65F25)

Related Items (4)

Sparse matrices ⋮ Ordered and periodic chaos of the bounded one-dimensional multibarrier potential ⋮ A survey of Lanczos procedures for very large real 'symmetric' eigenvalue problems ⋮ On the computation of a very large number of eigenvalues for selfadjoint elliptic operators by means of multigrid methods

Cites Work

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• Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
• Computing eigenvalues of very large symmetric matrices. An implementation of a Lanczos algorithm with no reorthogonalization
• Eigenvalues of perturbed Hermitian matrices
• Solution of Sparse Indefinite Systems of Linear Equations
• Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix
• Use of the Lanczos Method for Finding Complete Sets of Eigenvalues of Large Sparse Symmetric Matrices
• The Lanczos Algorithm with Selective Orthogonalization
• Computational Variants of the Lanczos Method for the Eigenproblem
• Methods of conjugate gradients for solving linear systems

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