  The least square solution of minimum norm of a rectangular linear system of
equations can be found out iteratively by using matrix splittings. However, the
convergence of such an iteration scheme arising out of a matrix splitting is
practically very slow in many cases. Thus, works on improving the speed of the
iteration scheme have attracted great interest. In this direction, comparison
of the rate of convergence of the iteration schemes produced by two matrix
splittings is very useful. But, in the case of matrices having many matrix
splittings, this process is time-consuming. The main goal of the current
article is to provide a solution to the above issue by using proper
multisplittings. To this end, we propose a few comparison theorems for proper
weak regular splittings and proper nonnegative splittings first. We then derive
convergence and comparison theorems for proper multisplittings with the help of
the theory of proper weak regular splittings.
