Convergence theorems for parallel alternating iterative methods

摘要

The parallel multisplitting nonstationary iterative Model A was introduced by Bru, Elsner, and Neumann [Linear Algebra Appl. 103 (1988) 175–192] for solving nonsingular linear system Ax=b using a weak nonnegative multisplitting of the first type. In this paper new results using a weak nonnegative multisplitting of the second type are introduced when A is a monotone matrix, and using P-regular multisplitting when A is a symmetric positive definite matrix. Combining Model A and alternating iterative methods, two new models of parallel multisplitting nonstationary iterations are introduced. It is shown that when matrix A is monotone and the multisplittings are weak nonnegative of the first or second type, both models lead to convergent schemes. When matrix A is symmetric positive definite and the multisplittings are P-regular, the schemes are also convergent.