This paper concerns methods for computing a few (5-10) interior eigenvalues and associated eigenvectors of a family of structured large sparse real symmetric indefinite matrices with off-diagonal entries equal to the off-diagonal entries of the 7-point central difference approximation of the three-dimensional Poisson equation on the unit cube with periodic boundary conditions and with suitably chosen random numbers (different for different matrices of the family) as main diagonal entries.
It is shown experimentally for the present problem that the Lancos algorithm in the implementation of J. Cullum and R. A. Willoughby [Lanczos algorithms for large symmetric eigenvalue computations. Vol. 1: Theory; Vol. 2: Programs (1985; Zbl 0574.65028)] is faster and more memory efficient than a sparse hybrid tridiagonalization method as well as the implicitly restarted Arnoldi method coupled with polynomial acceleration and in shift-and-invert mode with several direct and invert solvers.