In this talk we consider the use of {H}-matrix technique in the numerical solution of large eigenvalue problems, arising from a finite rank discretization of an integral operator. Its aim is two-fold. Firstly, deduce expressions for the approximate degenerate kernels as well as for their error bounds. Secondly, access HLIB library (Hierarchical matrices LIBrary) that provides, among others, routines for the construction of hierarchical matrix structures and arithmetic algorithms to perform matrix operations and (ii) to incorporate these routines into SLEPc library (Scalable Library for Eigenvalue Problem Computations) in order to explore its distributed processing capability as well as the plethora of algorithms available to solve eigenvalue problems.

This work was done with the collaboration of A. L. Nunes, J. E. Roman and M. Ahues.