Monte Carlo determination of multiple extremal eigenpairs.
Phys Rev E Stat Nonlin Soft Matter Phys
; 80(4 Pt 2): 046704, 2009 Oct.
Article
em En
| MEDLINE
| ID: mdl-19905479
ABSTRACT
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow et al, and exploited a sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings. We illustrate the effectiveness of the algorithm by its determination of the two largest eigenvalues of the transfer matrices for variously sized two-dimensional, zero-field Ising models. While very likely useful for other transfer-matrix problems, the algorithm is however quite general and should find application to a larger variety of problems requiring a few dominant eigenvalues of a matrix.
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01-internacional
Base de dados:
MEDLINE
Assunto principal:
Algoritmos
/
Análise Numérica Assistida por Computador
/
Método de Monte Carlo
/
Modelos Estatísticos
Tipo de estudo:
Health_economic_evaluation
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Risk_factors_studies
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Assunto da revista:
BIOFISICA
/
FISIOLOGIA
Ano de publicação:
2009
Tipo de documento:
Article
País de afiliação:
Estados Unidos