Abstract
Comparison theorems between the spectral radii of different matrices are a useful tool for judging the efficiency of preconditioners. For single splittings of different monotone matrices, Elsner et al. (Linear Algebra Appl. 363:65–80, 2003) gave out comparison theorems for spectral radii. For double splittings, some convergence and comparison theorems of a monotone matrix are presented by Shen et al. (Comput. Math. Appl. 51:1751–1760, 2006). In this note we give the comparison theorem for the spectral radii of matrices arising from double splittings of different monotone matrices.
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