Sequential and parallel synchronous alternating iterative methods
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Título: | Sequential and parallel synchronous alternating iterative methods |
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Autor/es: | Climent, Joan-Josep | Perea Marco, Mari Carmen | Tortosa, Leandro | Zamora, Antonio |
Grupo/s de investigación o GITE: | Criptología y Seguridad Computacional |
Centro, Departamento o Servicio: | Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad de Alicante. Departamento de Ciencia de la Computación e Inteligencia Artificial |
Palabras clave: | Nonsingular matrix | Iterative method | Spectral radius | Splitting | Multisplitting | Alternating method | Stationary method | Nonstationary method | Convergence conditions | Comparison conditions |
Área/s de conocimiento: | Álgebra | Ciencia de la Computación e Inteligencia Artificial |
Fecha de publicación: | 24-nov-2003 |
Editor: | American Mathematical Society |
Cita bibliográfica: | CLIMENT, Joan-Josep, et al. “Sequential and parallel synchronous alternating iterative methods”. Mathematics of Computation. Vol. 73, No. 246 (2003). ISSN 0025-5718, pp. 691-717 |
Resumen: | The so-called parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra and its Applications 103:175-192 (1988)] for solving a nonsingular linear system Ax = b using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when A is a monotone matrix using a weak nonnegative multisplitting of the second type and when A is a symmetric positive definite matrix using a P -regular multisplitting. Also, nonstationary alternating iterative methods are studied. Finally, combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. When matrix A is monotone and the multisplittings are weak nonnegative of the first or of the second type, both models lead to convergent schemes. Also, when matrix A is symmetric positive definite and the multisplittings are P -regular, the schemes are also convergent. |
URI: | http://hdl.handle.net/10045/25282 |
ISSN: | 0025-5718 (Print) | 1088-6842 (Online) |
DOI: | 10.1090/S0025-5718-03-01607-7 |
Idioma: | eng |
Tipo: | info:eu-repo/semantics/article |
Derechos: | First published in Math. Comp. 73 (2004), published by the American Mathematical Society. |
Revisión científica: | si |
Versión del editor: | http://dx.doi.org/10.1090/S0025-5718-03-01607-7 |
Aparece en las colecciones: | INV - CSC - Artículos de Revistas INV - GAG - Artículos de Revistas INV - ANVIDA - Artículos de Revistas |
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