A study on decomposition methods

AbstractAn innovative decomposition method for the approximate solution of problems is introduced based upon successive projection approximations derived in [1]. The new method provides substantially greater freedom for decomposing a given problem into a collection of subproblems than conventional methods [4]. An approximation can be approached by recursively searching in the collection of subproblems along a chosen search path. When applied to partial differential equations, the partitioning can be made in either the physical domain (domain decomposition) of a partial differential equation or in the associated linear space (space decomposition). The decompositions can be used to solve large-scale problems, to develop parallel algorithms and novel iterative techniques