- AutorIn
- Peter Benner
- Thomas Mach
- Titel
- On the QR Decomposition of H-Matrices
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:ch1-200901420
- Schriftenreihe
- Chemnitz Scientific Computing Preprints
- Bandnummer
- 09-04
- ISSN
- 1864-0087
- Abstract (EN)
- The hierarchical (<i>H-</i>) matrix format allows storing a variety of dense matrices from certain applications in a special data-sparse way with linear-polylogarithmic complexity. Many operations from linear algebra like matrix-matrix and matrix-vector products, matrix inversion and LU decomposition can be implemented efficiently using the <i>H</i>-matrix format. Due to its importance in solving many problems in numerical linear algebra like least-squares problems, it is also desirable to have an efficient QR decomposition of <i>H</i>-matrices. In the past, two different approaches for this task have been suggested. We will review the resulting methods and suggest a new algorithm to compute the QR decomposition of an <i>H</i>-matrix. Like other <i>H</i>-arithmetic operations the <i>H</i>QR decomposition is of linear-polylogarithmic complexity. We will compare our new algorithm with the older ones by using two series of test examples and discuss benefits and drawbacks of the new approach.
- Andere Ausgabe
- Link: http://www.tu-chemnitz.de/mathematik/csc/preprints.php
- Freie Schlagwörter
- HQR decomposition
- QR decomposition
- least squares problem
- matrix factorisation
- Klassifikation (DDC)
- 510
- Normschlagwörter (GND)
- Hierarchische Matrix
- Orthogonalisierung
- Publizierende Institution
- Technische Universität Chemnitz, Chemnitz
- Förder- / Projektangaben
- URN Qucosa
- urn:nbn:de:bsz:ch1-200901420
- Veröffentlichungsdatum Qucosa
- 28.08.2009
- Dokumenttyp
- Preprint
- Sprache des Dokumentes
- Englisch