Results 121 to 130 of about 5,496,658 (160)

Two-Sided Arnoldi and Nonsymmetric Lanczos Algorithms

SIAM Journal on Matrix Analysis and Applications, 2002
The paper proposes a new two-sided block Arnoldi recursion in order to define a model reduction procedure for large, linear, time-invariant, multi-input/multi-output differential algebraic systems. This procedure is proved to have maximum block moment properties.
Cullum, Jane, Zhang, Tong
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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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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 ...
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Modified explicitly restarted Lanczos algorithm

Computer Physics Communications, 1998
Convergence acceleration and optimization in computing eigenvectors and eigenvalues of very large sparse matrices is obtained by the modified explicitly restarted Lanczos method. The proposed algorithm can calculate the multiplicities of eigenvalues, the required memory is small, and it can be easily implemented.
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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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BiCG/QMR and Lanczos algorithms

2020
In this chapter we describe Krylov methods using short recurrences, like Lanczos algorithms, BiCG, and QMR which use biorthogonal bases of the Krylov subspaces.
Gérard Meurant, Jurjen Duintjer Tebbens
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Implicitly restarted Lanczos algorithm for model reduction

Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), 2002
The Lanczos algorithm is increasingly used for model reduction of large scale stable systems. Two features of the algorithm, however, limit its applicability: the tendency of the reduced model to poorly approximate low frequency dynamics, and the fact that the approximation is not guaranteed to be stable.
Vasilios Papakos, Imad M. Jaimoukha
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Analysis of the Lanczos Error Bounds and Its Application to the Explicitly Restarted Lanczos Algorithm

2002
LExpRes is a k-step explicit restart variant of the Lanczos algorithm. In this method a periodic/selective reorthogonalization strategy is adopted in order to dampen the affects of instability incurred by a loss of orthogonality among the Lanczos vectors.
A. Cooper, Marek Szularz, Jim Weston
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Explicitly restarted Lanczos algorithms in an MPP environment

Parallel Computing, 1999
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Marek Szularz, Jim Weston, Maurice Clint
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A highly parallel explicitly restarted Lanczos algorithm

1996
The Lanczos algorithm is one of the principal methods for the computation of a few of the extreme eigenvalues and their corresponding eigenvectors of large, usually sparse, real symmetric matrices. In this paper a single-vector Lanczos method based on a simple restarting strategy is proposed.
Marek Szularz, Jim Weston, Maurice Clint, Kieran Murphy   +3 more
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