Memory-Saving Technique for the Sakurai-Sugiura Eigenvalue Solver Using the Shifted Block Conjugate Gradient Method

In recent years, a numerical quadrature-based sparse eigensolver-the so-called Sakurai-Sugiura method-and its variants have attracted attention because of their highly coarse-grained parallelism. In this paper, we propose a memory-saving technique for a variant of the Sakurai-Sugiura method. The proposed technique can be utilized when inner linear systems are solved with the shifted block conjugate gradient method. Using our technique, eigenvalues and residual norms can be obtained without the explicit need to compute the eigenvector. This technique saves a considerable amount of memory space when eigenvectors are unnecessary. Our technique is also beneficial in cases where eigenvectors are necessary, because the residual norms of the target eigenpairs can be cheaply computed and monitored during each iteration step of the inner linear solver.