Simple non-extensive sparsification of the hierarchical matrices
For researchers working on hierarchical matrix solvers, this offers a new approach to sparsification, but it is incremental as it builds on existing H2 methods.
The paper proposes a non-extensive sparse factorization for H2 matrices, enabling substitution of direct H2 solution with a sparse system of the same size. Numerical experiments show consistency compared to HODLR, H2Lib, and IFMM.
In this paper, we consider the matrices approximated in H2 format. The direct solution, as well as the preconditioning, of systems with such matrices is a challenging problem. We propose a non-extensive sparse factorization of the H2 matrix that allows to substitute the direct H2 solution with the solution of the system with an equivalent sparse matrix of the same size. The sparse factorization is constructed out of parameters of the H2 matrix. In the numerical experiments, we show the consistency of this approach in comparison to the other approximate block low-rank hierarchical solvers, such as HODLR, H2Lib and IFMM.