Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR2S Format - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Matrix Analysis and Applications Year : 2021

Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR2S Format

Cleve Ashcraft
  • Function : Author
  • PersonId : 1086124
Théo Mary

Abstract

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.
Fichier principal
Vignette du fichier
BLR2.pdf (556.63 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03070416 , version 1 (15-12-2020)
hal-03070416 , version 2 (22-03-2021)

Identifiers

Cite

Cleve Ashcraft, Alfredo Buttari, Théo Mary. Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR2S Format. SIAM Journal on Matrix Analysis and Applications, 2021, 42 (2), ⟨10.1137/20M1386451⟩. ⟨hal-03070416v2⟩
402 View
417 Download

Altmetric

Share

Gmail Facebook X LinkedIn More