A new type of matrix splitting and its applications

A possible type of the matrix splitting is introduced. Using this matrix splitting, we introduce a few properties and representations of generalized inverses as well as iterative methods for computing various solutions of singular linear systems. This matrix splitting is a generalization of the known index splitting from [13] and a proper splitting from [4]. Using a generalization of the condition number and introduced representations of generalized inverses, we obtain several norm estimates.