Climent, Joan-Josep, Perea Marco, Mari Carmen, Tortosa, Leandro, Zamora, Antonio
Sequential and parallel synchronous alternating iterative methods
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
URI: http://hdl.handle.net/10045/25282
DOI: 10.1090/S0025-5718-03-01607-7
ISSN: 0025-5718 (Print)
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 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.
Keywords:Nonsingular matrix, Iterative method, Spectral radius, Splitting, Multisplitting, Alternating method, Stationary method, Nonstationary method, Convergence conditions, Comparison conditions
American Mathematical Society
info:eu-repo/semantics/article