Abstract:

The rank deficient linear systemÂx=b  is augmented to a block 4×4 linear system Âη=b´, where A is a square matrix, then A is split with PSD subproper splitting. The necessary and sufficient condition for the PSD method being semiconvergent is obtained. Finally a method is provided to compute the least square solution of minimal norm to ]Ax=b and exmamples are given to illustrate the process, whereA∈C^m×nb∈C^m,b´∈C ^m+n

Key words: PSD splitting; Semiconvergent; Least square solution; Moore-Penrose generalized inverse