Iterative cluster aggregation methods for systems of linear equations (Q1385917)

We distinguish a class of iterative methods with a special organization of computations that is typical for classic block methods. After preliminary processing (e.g., after scaling), the equations of a system are aggregated into separate groups, and the same equation can be contained in distinct groups, which we call clusters. For a symmetric linear system of equations, we show that the iterative cluster aggregation methods converge. We present examples of methods that are associated with methods of point and block relaxation, block iterative methods, iterative methods of multicolor partition, etc. Among the most important examples of cluster aggregation methods, we note iterative domain decomposition methods of Schwarz type.