New comparison results for parallel multisplitting iterative methods

The parallel multisplitting nonstationary iterative Model A and Models 1-2 were introduced by Bru et al. [Bru, Elsner, Neumann, Models of parallel chaotic iteration methods, Linear Algebra Appl. 103 (1988) 175-192], and Climent et al. [Climent, Perea, Tortosa, Zamora, Convergence theorems for parallel alternating iterative methods, Appl. Math. Comput. 148 (2004) 497-517], respectively. Using nonnegative splitting theory, we present some new comparison theorems between two general parallel multisplittings of Model A and Models 1-2 when the coefficient matrix is a monotone matrix. Particularly, we establish some sufficient conditions for strict inequalities in comparisons of spectral radii of different iteration matrices.