Sequential and parallel synchronous alternating iterative methods |
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| Authors: | Joan-Josep Climent Carmen Perea Leandro Tortosa Antonio Zamora |
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| Institution: | Departament de Ciència de la Computació i Intel$·$ligència Artificial, Universitat d'Alacant, Ap. Correus 99, E--03080 Alacant, Spain ; Departamento de Estadística y Matemática Aplicada, Universidad Miguel Hernández, Escuela Politécnica Superior de Orihuela, E-03550, Orihuela, Spain ; Departament de Ciència de la Computació i Intel$·$ligència Artificial, Universitat d'Alacant, Ap. Correus 99, E--03080 Alacant, Spain ; Departament de Ciència de la Computació i Intel$·$ligència Artificial, Universitat d'Alacant, Ap. Correus 99, E--03080 Alacant, Spain |
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| Abstract: | 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  using a weak nonnegative multisplitting of the first type. In this paper new results are introduced when  is a monotone matrix using a weak nonnegative multisplitting of the second type and when  is a symmetric positive definite matrix using a  -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  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  is symmetric positive definite and the multisplittings are  -regular, the schemes are also convergent. |
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| Keywords: | Nonsingular matrix iterative method spectral radius splitting multisplitting alternating method stationary method nonstationary method convergence conditions comparison conditions |
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