Results 161 to 170 of about 16,479 (201)

GPU Accelerated Lanczos Algorithm with Applications

2011 IEEE Workshops of International Conference on Advanced Information Networking and Applications, 2011
Graphics 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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The nonsymmetric Lanczos algorithm and controllability

Systems & Control Letters, 1991
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Boley, Daniel, Golub, Gene
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Yet another block Lanczos algorithm

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation, 2010
A new block Lanczos algorithm for computations over small finite fields is presented and analysed. The algorithm can be used to solve a system of linear equations or sample uniformly from the null space whenever the number of nilpotent blocks with order at least two in the Jordan form of the given coefficient matrix is less than the block factor on the
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The Lanczos-Arnoldi algorithm and controllability

Systems & Control Letters, 1984
The controllable subspace of linear systems described by the mathematical model \(\dot x=Ax+Bu\) is usually determined by the so-called staircase algorithm. In order to apply this method, it is necessary to store the matrix A as a full matrix, even if it is large and sparse.
Boley, D. L., Golub, G. H.
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Projective Block Lanczos Algorithm for Dense, Hermitian Eigensystems

Journal of Computational Physics, 1996
The authors introduce the projective block Lanczos (PBL) algorithm for seeking extreme eigenvalues and eigenvectors of an \(N\times N\) Hermitian matrix and present examples and applications on various physical problems. The first example is drown from many-body quantum mechanics, specifically, clusters of magnetic dipoles.
Webster, Frank, Lo, Gen-Ching
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An adaptive block Lanczos algorithm

Numerical Algorithms, 1996
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.
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Fast Estimation of Principal Eigenspace Using Lanczos Algorithm

SIAM Journal on Matrix Analysis and Applications, 1994
Let \(B\) denote a positive semidefinite Hermitian matrix of the order \(m\) and rank \(d\) with \(d\) much less than \(m\). Starting with simple but surprisingly powerful observations, the authors first show that for any real number \(\sigma\), the Lanczos algorithm applied to the matrix \(A= B+ \sigma I\) may be used to determine the range of \(B ...
Xu, Guanghan, Kailath, Thomas
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A Lanczos Algorithm with Restarts

1987
The Lanczos algorithm, originally devised to tridiagonalize a matrix, is used for the generalized eigenvalue problem to operate on a whole subspace, yielding a block-tridiagonal matrix in the Krylov sequence of subspaces. To use prior information and enhance convergence, a subspace restart formulation is introduced. Global orthogonality of the iterated
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Misconvergence in the Lanczos algorithm

1990
Abstract The Lanczos algorithm generates Ritz values in order to approximate eigenvalues. If some eigenvalues are clustered then a Ritz value may hover at a wrong value for a good number of steps. We study this phenomenon and focus on the point of discovery, the first step at which it is certain that there is a hidden eigenvalue in the ...
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An Efficient Implementation of the Nonsymmetric Lanczos Algorithm

SIAM Journal on Matrix Analysis and Applications, 1997
Summary: 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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