Hierarchical matrix (H-matrix) techniques can be used to efficiently treat dense matrices. With an H-matrix, the storage
requirements and performing all fundamental operations, namely matrix-vector multiplication, matrix-matrix multiplication and matrix inversion
can be done in almost linear complexity.
In this work, we tried to gain even further
speedup for the H-matrix arithmetic by utilizing multiple processors. Our approach towards an H-matrix distribution
relies on the splitting of the index set.
The main results achieved in this work based on the index-wise H-distribution are: A highly scalable algorithm for the H-matrix truncation and matrix-vector multiplication, a scalable algorithm for the H-matrix matrix multiplication, a limited scalable algorithm for the H-matrix inversion for a large number of processors.
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa.de:bsz:15-qucosa-101164 |
| Date | 11 December 2012 |
| Creators | Izadi, Mohammad |
| Contributors | Max Planck Institute for Mathematics in the Sciences (MIS), Scientific Computing, Prof. Dr. Dre. h.c. Wolfgang Hackbusch, Prof. Dr. Gerhard Zumbusch |
| Publisher | Universitätsbibliothek Leipzig |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | doc-type:doctoralThesis |
| Format | application/pdf |
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