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

DOI10.1137/20M1386451MaRDI QIDQ4997842

Cleve Ashcraft, Alfredo Buttari, Theo A. Mary

Publication date: 30 June 2021

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

numerical linear algebrahierarchical matricesblock low-rank matricesblock separable matricesdata sparse matricesLu factorization

Mathematics Subject Classification ID

Roundoff error (65G50) Direct numerical methods for linear systems and matrix inversion (65F05)

Uses Software

• MUMPS
• SparseMatrix

Cites Work

• A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
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• Introduction to hierarchical matrices with applications.
• A fast block low-rank dense solver with applications to finite-element matrices
• Domain decomposition based \({\mathcal H}\)-LU preconditioning
• Hierarchical Matrices: Algorithms and Analysis
• The university of Florida sparse matrix collection
• Fast algorithms for hierarchically semiseparable matrices
• Solving block low-rank linear systems by LU factorization is numerically stable
• Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic
• Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
• Improving Multifrontal Methods by Means of Block Low-Rank Representations
• A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
• On the Complexity of the Block Low-Rank Multifrontal Factorization
• Bridging the Gap Between Flat and Hierarchical Low-Rank Matrix Formats: The Multilevel Block Low-Rank Format

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