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Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem
, 1980 C. Paige
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On estimating the largest eigenvalue with the Lanczos algorithm
, 1982 B. Parlett, H. Simon, Lynd M. Stringer
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A Look Ahead Lanczos Algorithm for Unsymmetric Matrices
, 1985 B. Parlett, D. Taylor, Zhishun A. Liu
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An adaptive block Lanczos algorithm
Numerical Algorithms, 1996The 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.
Qiang Ye, Ye Qiang
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A rational Lanczos algorithm for model reduction
Numerical Algorithms, 1996This paper uses Lanczos techniques for the reduced-order modeling of large scale dynamical single input-single output systems defined by the state space equations \(Edx/dt =Ax(t) +bu(t)\) and \(y(t)= c^Tx(t) +du(t)\). The matrices \(A\) and \(E\) are assumed to be sparse or structured (e.g. Toeplitz).
K Gallivan, P Van Dooren
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The nonsymmetric Lanczos algorithm and controllability
Systems and Control Letters, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel Boley, Gene H Golub
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An Efficient Implementation of the Nonsymmetric Lanczos Algorithm
SIAM Journal on Matrix Analysis and Applications, 1997Summary: Lanczos vectors computed in finite precision arithmetic by the three-term recurrence tend to lose their mutual biorthogonality. One either accepts this loss and takes more steps or re-biorthogonalizes the Lanczos vectors at each step. For the symmetric case, there is a compromise approach.
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An Improved Lanczos Algorithm for Principal Component Analysis
Proceedings of 2020 6th International Conference on Computing and Data Engineering, 2020In this paper, we propose an improved Lanczos algorithm for principal component analysis. This algorithm is to get a low rank approximation which is identical to truncated singular valued decomposition, but it is much cheaper. Since this algorithm is only an extension of Lanczos algorithm to improve its approximation capabilities, we call it extended ...
Xuansheng Wang +5 more
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GPU Accelerated Lanczos Algorithm with Applications
2011 IEEE Workshops of International Conference on Advanced Information Networking and Applications, 2011Graphics Processing Units provide a large computational power at a very low price which position them as an ubiquitous accelerator. GPGPU is accelerating general purpose computations using GPU's. GPU's have been used to accelerate many Linear Algebra routines and Numerical Methods.
Kiran Kumar Matam, Kishore Kothapalli
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