Robust parallel Lanczos methods for clustered eigenvalues

1997 ◽  
pp. 710-717 ◽  
Author(s):  
M. Szularz ◽  
J. Weston ◽  
M. Clint
Keyword(s):  
Clustered Eigenvalues ◽  
Lanczos Methods

scholarly journals Iterative Methods for the Computation of the Perron Vector of Adjacency Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1522
Author(s):  
Anna Concas ◽  
Lothar Reichel ◽  
Giuseppe Rodriguez ◽  
Yunzi Zhang
Keyword(s):  
Iterative Methods ◽  
Adjacency Matrix ◽  
Lanczos Method ◽  
Power Method ◽  
Arnoldi Method ◽  
Multiple Eigenvalues ◽  
Computer Storage ◽  
Adjacency Matrices ◽  
Lanczos Methods ◽  
Perron Vector

The power method is commonly applied to compute the Perron vector of large adjacency matrices. Blondel et al. [SIAM Rev. 46, 2004] investigated its performance when the adjacency matrix has multiple eigenvalues of the same magnitude. It is well known that the Lanczos method typically requires fewer iterations than the power method to determine eigenvectors with the desired accuracy. However, the Lanczos method demands more computer storage, which may make it impractical to apply to very large problems. The present paper adapts the analysis by Blondel et al. to the Lanczos and restarted Lanczos methods. The restarted methods are found to yield fast convergence and to require less computer storage than the Lanczos method. Computed examples illustrate the theory presented. Applications of the Arnoldi method are also discussed.

Parallel computation of arbitrarily shaped waveguide modes using BI-RME and Lanczos methods

2006 ◽  
Vol 23 (4) ◽  
pp. 273-284
Author(s):  
A. M. Vidal ◽  
A. Vidal ◽  
V. E. Boria ◽  
V. M. García
Keyword(s):  
Parallel Computation ◽  
Waveguide Modes ◽  
Lanczos Methods

A matrix analysis of Arnoldi and Lanczos methods

1998 ◽  
Vol 81 (1) ◽  
pp. 125-141 ◽  
Author(s):  
V. Simoncini
Keyword(s):  
Matrix Analysis ◽  
Lanczos Methods

KRYLOV-LANCZOS METHODS

2001 ◽  
pp. 691-698
Author(s):  
R.R. Craig
Keyword(s):  
Lanczos Methods

scholarly journals Strategies for spectrum slicing based on restarted Lanczos methods

2012 ◽  
Vol 60 (2) ◽  
pp. 279-295 ◽  
Author(s):  
Carmen Campos ◽  
Jose E. Roman
Keyword(s):  
Spectrum Slicing ◽  
Lanczos Methods
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