A classic mathematical technique, the Schwarz Alternating Method (SAM), has recently attracted much attention from researchers in the field of parallel computations, as well as theoreticians. Its advantages in parallelism, wide applicability and great flexibility in implementation make SAM a competitive choice in parallel computations. However, the computational performance of the classical SAM and its modern extensions strongly depend on the amount of overlap between the neighboring subregions. Introducing a large overlap has changed the image of SAM from an impractical theoretical technique to a rewarding numerical approach. However, the duplication of work in these overlapped regions is undesirable. Reducing the amount of overlap without affecting the speed of convergence has become an important performance issue.Schwarz Splitting (SS) has been proposed as an extension of SAM in numerical linear algebra, and a generalized SS is presented in this paper. The new approach allows utilization of the flexibi...