Overlapping vs partitioning in block-iteration methods: Application in large-scale system theory (Q1119221)

Ideas of ``overlapping'' are introduced to the theory of decomposition and coordination. Through overlapping it is proposed to examine decomposition after ``remodelling'' the system in such a way as to depict a weakly coupled configuration. After introducing the concept of overlapping in linear splitting theory the paper deals with large-scale systems theory. Matrix splitting, Hamiltonian operator splitting and Riccati operator splitting are successively considered for the case of block-overlapping and are compared with classical corresponding splitting methods based on block partitioning. Numerical simulations are given. Overlapping decomposition is shown to succeed where classical partitioning decomposition fails.