Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR^2 Format
| Autor: | Alfredo Buttari, Théo Mary, Cleve Ashcraft |
|---|---|
| Přispěvatelé: | ANSYS, Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées, Performance et Qualité des Algorithmes Numériques (PEQUAN), Laboratoire d'Informatique de Paris 6 (LIP6), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Centre National de la Recherche Scientifique (CNRS), LIP6 |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Rank (linear algebra)
Astrophysics::High Energy Astrophysical Phenomena 010103 numerical & computational mathematics Astrophysics::Cosmology and Extragalactic Astrophysics computer.software_genre 01 natural sciences law.invention Separable space Matrix (mathematics) law numerical linear algebra [INFO]Computer Science [cs] 0101 mathematics [MATH]Mathematics [math] Column (data store) Astrophysics::Galaxy Astrophysics Mathematics Block (data storage) Discrete mathematics hierarchical matrices Numerical linear algebra block low-rank matrices Special class LU decomposition Data sparse matrices LU factorization computer Analysis block separable matrices |
| Zdroj: | SIAM Journal on Matrix Analysis and Applications SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, In press |
| ISSN: | 0895-4798 1095-7162 |
| Popis: | International audience; We investigate a special class of data sparse rank-structured matrices that combine a flat block low-rank (BLR) partitioning with the use of shared (called nested in the hierarchical case) bases. This format is to H 2 matrices what BLR is to H matrices: we therefore call it the BLR 2 matrix format. We present algorithms for the construction and LU factorization of BLR 2 matrices, and perform their cost analysis-both asymptotically and for a fixed problem size. With weak admissibility, BLR 2 matrices reduce to block separable matrices (the flat version of HBS/HSS). Our analysis and numerical experiments reveal some limitations of BLR 2 matrices with weak admissibility, which we propose to overcome with two approaches: strong admissibility, and the use of multiple shared bases per row and column. |
| Databáze: | OpenAIRE |
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