An adaptive block Lanczos algorithm
type: Item
instance of: scholarly article
title: An adaptive block Lanczos algorithm
zbMATH Open document ID: 0859.65032
DOI: 10.1007/BF02141743
author: Qiang Ye
published in: Numerical Algorithms
publication date: 1997-04-07T00:00:00Z
review text: The paper is devoted to a generalization of the block Lanczos algorithm for a symmetric matrix, which allows the block size to be increased during the iterative process. In particular, the algorithm can be implemented with the block size chosen adaptively according to the clustering of Ritz values. The author considers an approach that is based on a single run of the algorithm. The adaptive algorithm, which is proposed, tests the clustering of Ritz values at each step and increases the block size when it is found inadequate. In this way all multiple and clustered eigenvalues can be found and the difficulty of choosing the block size is eased. Residual bounds for clustered eigenvalues are given. Numerical examples illustrate the adaptive algorithm.
Mathematics Subject Classification ID: 65F15
zbMATH DE Number: 915385
zbMATH Keywords: numerical examples
zbMATH Keywords: block Lanczos algorithm
zbMATH Keywords: symmetric matrix
zbMATH Keywords: Ritz values
zbMATH Keywords: adaptive algorithm
zbMATH Keywords: clustered eigenvalues
describes a project that uses: na1
MaRDI profile type: Publication
cites work: Avoiding breakdown and near-breakdown in Lanczos type algorithms
cites work: Fourier Analysis of Iterative Methods for Elliptic pr
cites work: Q4192888
cites work: Q3692703
cites work: An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
cites work: Reorthogonalization and Stable Algorithms for Updating the Gram-Schmidt QR Factorization
cites work: The Spectral Transformation Lanczos Method for the Numerical Solution of Large Sparse Generalized Symmetric Eigenvalue Problems
cites work: Q4194451
cites work: Q5185900
cites work: A Shifted Block Lanczos Algorithm for Solving Sparse Symmetric Generalized Eigenproblems
cites work: A Completed Theory of the Unsymmetric Lanczos Process and Related Algorithms, Part I
cites work: Q3868672
cites work: The use of a refined error bound when updating eigenvalues of tridiagonals
cites work: The Lanczos Algorithm with Selective Orthogonalization
cites work: On Estimating the Largest Eigenvalue with the Lanczos Algorithm
cites work: A Look-Ahead Lanczos Algorithm for Unsymmetric Matrices
cites work: On the Rates of Convergence of the Lanczos and the Block-Lanczos Methods
cites work: The Lanczos Algorithm With Partial Reorthogonalization
cites work: The convergence behavior of Ritz values in the presence of close eigenvalues
cites work: A Convergence Analysis for Nonsymmetric Lanczos Algorithms
cites work: A Breakdown-Free Variation of the Nonsymmetric Lanczos Algorithms
full work available at URL: https://doi.org/10.1007/bf02141743
OpenAlex ID: W2015768950
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description: scientific article; zbMATH DE number 915385