TY - JOUR
TI - Sequential and parallel synchronous alternating iterative methods
AU - Climent, Joan-Josep
AU - Perea Marco, Mari Carmen
AU - Tortosa, Leandro
AU - Zamora, Antonio
DA - 2003-11-24
UR - http://hdl.handle.net/10045/25282
AB - 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.
KW - Nonsingular matrix
KW - Iterative method
KW - Spectral radius
KW - Splitting
KW - Multisplitting
KW - Alternating method
KW - Stationary method
KW - Nonstationary method
KW - Convergence conditions
KW - Comparison conditions
DO - 10.1090/S0025-5718-03-01607-7
SN - 0025-5718 (Print)
PB - American Mathematical Society
ER -