Preconditioners for hierarchical matrices
We continue to develop our h2tools package with the new functionality.
The solution of linear systems with hierarchical matrices plays a crucial role in many applications.
We use the sparse extended form of the H2-matrices to reduce the initial linear system to a block-structured
linear system and then use this block structure to construct different preconditioners. The most efficient
preconditioner is the preconditioner based on the
so-called “reverse-Schur complement” method: we solve
the initial system using the availability of the fast matrix-by-vector product, and to solve the corretion equation
we construct the extended system and make several preconditioned iterative steps with it.