Back to Search
Start Over
Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR^2 Format
- Source :
- SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, In press
- Publication Year :
- 2020
- Publisher :
- HAL CCSD, 2020.
-
Abstract
- 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.
- Subjects :
- 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
Subjects
Details
- Language :
- English
- ISSN :
- 08954798 and 10957162
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Matrix Analysis and Applications, SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, In press
- Accession number :
- edsair.doi.dedup.....fecb1ae5c38c8f29d9e1f7789ab3f8c4