On the Schwarz alternating method for eigenvalue problems

In this paper an analogue of the Schwarz alternating method is considered and a minimal eigenvalue and its corresponding eigenvector of the generalized symmetric eigenvalue problem are found. The technique suggested is based on decomposition of the original domain into overlapping subdomains and on consideration of local eigenvalue problems in subdomains. Both multiplicative and additive variations of the method are constructed and studied. It is shown that a discretization of the multiplicative variation of the Schwarz method is equivalent to the block coordinate relaxation method. An additive variation of the method is suitable for realization on parallel architecture.