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Article Dans Une Revue SIAM Journal on Matrix Analysis and Applications Année : 2021

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

Cleve Ashcraft
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Théo Mary

Résumé

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.
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Dates et versions

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

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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⟩
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