A UNIFIED FRAMEWORK FOR THE CONSTRUCTION OF VARIOUS MATRIX MULTISPLITTING ITERATIVE METHODS FOR LARGE SPARSE SYSTEM OF LINEAR-EQUATIONS

A unified framework for the construction of various synchronous and as ynchronous parallel matrix multisplitting iterative methods, suitable to the SIMD and MIMD multiprocessor systems, respectively, is presente d, and its convergence theory is established under rather weak conditi ons. These afford general method models and systematical convergence c riterions for studying the parallel iterations in the sense of matrix multisplitting. In addition, how the known parallel matrix multisplitt ing iterative methods can be classified into this new framework, and w hat novel ones can be generated by it are shown in detail.