  Matrix double splitting iterations are simple in implementation while solving
real non-singular (rectangular) linear systems. In this paper, we present two
Alternating Double Splitting (ADS) schemes formulated by two double splittings
and then alternating the respective iterations. The convergence conditions are
then discussed along with comparative analysis. The set of double splittings
used in each ADS schemes induce a preconditioned system which helps in showing
the convergence of the ADS schemes. We also show that the classes of matrices
for which one ADS scheme is better than the other are mutually exclusive.
Numerical experiments confirm the proposed ADS schemes are superior to the
existing methods in actual implementation. Though the problems are considered
in the rectangular matrix settings, the same problems are even new in
non-singular matrix settings.
