On the Schwarz Alternating Method for Eigenvalue Problems

In this paper an analogue of the Schwarz alternating method is considered to nd a minimal eigenvalue and its corresponding eigenvector of generalized symmetric eigenvalue problem. 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 variants of the method are constructed and studied. It is shown that a discretization of the multiplicative variant of the Schwarz method is equivalent to the block coordinate relaxation method. An additive variant of the method is suitable for realization on parallel architecture.