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. |