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.


26/05/2016 A TT-eigenvalue solver that finally works Papers
12/05/2016 Exponential machines and tensor trains Papers
06/04/2016 Convergence analysis of a projected fixed-point iteration Papers
30/03/2016 Compress-and-eliminate solver for sparse matrices Papers
01/12/2015 New paper in SIMAX Papers


We are located at the 2-nd floor of the new "Technopark-3” building in Skolkovo (few kilometers outside Moscow Ring Road). The building is accessible from Skolkovo Road (Сколковское шоссе) and Minskoe Highway (Минское шоссе).