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Matrix double splitting iterations are simple in implementation while solvingreal non-singular (rectangular) linear systems. In this paper, we present twoAlternating Double Splitting (ADS) schemes formulated by two double splittingsand then alternating the respective iterations. The convergence conditions arethen discussed along with comparative analysis. The set of double splittingsused in each ADS schemes induce a preconditioned system which helps in showingthe convergence of the ADS schemes. We also show that the classes of matricesfor which one ADS scheme is better than the other are mutually exclusive.Numerical experiments confirm the proposed ADS schemes are superior to theexisting methods in actual implementation. Though the problems are consideredin the rectangular matrix settings, the same problems are even new innon-singular matrix settings.

Alternating Stationary Iterative Methods Based on Double Splittings