Acoustic inverse scattering via Helmholtz operator factorization and optimization
Journal of Computational Physics
Extension and optimization of the FIND algorithm: Computing Green's and less-than Green's functions
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 0.01 |
In this paper we present a fast direct solver for certain classes of dense structured linear systems that works by first converting the given dense system to a larger system of block sparse equations and then uses standard sparse direct solvers. The kind of matrix structures that we consider are induced by numerical low rank in the off-diagonal blocks of the matrix and are related to the structures exploited by the fast multipole method (FMM) of Greengard and Rokhlin. The special structure that we exploit in this paper is captured by what we term the hierarchically semiseparable (HSS) representation of a matrix. Numerical experiments indicate that the method is probably backward stable.