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Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR^2 Format

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.
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https://hal.archives-ouvertes.fr/hal-03070416
Contributor : Theo Mary <>
Submitted on : Monday, March 22, 2021 - 7:02:06 PM
Last modification on : Tuesday, May 4, 2021 - 4:07:16 PM

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  • HAL Id : hal-03070416, version 2

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Cleve Ashcraft, Alfredo Buttari, Théo Mary. Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR^2 Format. SIAM Journal on Matrix Analysis and Applications, Society for Industrial and Applied Mathematics, In press. ⟨hal-03070416v2⟩

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