Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic

DOI10.1137/19M1255628OpenAlexW2980372014WikidataQ114074256 ScholiaQ114074256MaRDI QIDQ5203969

Claude-Pierre Jeannerod, Clément Pernet, Daniel S. Roche, Theo A. Mary

Publication date: 9 December 2019

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

Full work available at URL: https://doi.org/10.1137/19m1255628

zbMATH Keywords

linear algebrafast matrix arithmeticblock low-rank matrices

Mathematics Subject Classification ID

Factorization of matrices (15A23) Direct numerical methods for linear systems and matrix inversion (65F05) Numerical analysis (65-XX) Computer science (68-XX)

Related Items

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

Uses Software

• LAPACK
• MUMPS
• mctoolbox

Cites Work

• Unnamed Item
• Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions
• Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
• On a new class of structured matrices
• Existence of \(\mathcal H\)-matrix approximants to the inverse FE-matrix of elliptic operators with \(L^\infty\)-coefficients
• Time and space efficient generators for quasiseparable matrices
• Rank-profile revealing Gaussian elimination and the CUP matrix decomposition
• Fast linear algebra is stable
• Gaussian elimination is not optimal
• Hierarchical Matrices: Algorithms and Analysis
• Exploiting parallelism in matrix-computation kernels for symmetric multiprocessor systems
• Fast algorithms for hierarchically semiseparable matrices
• Powers of tensors and fast matrix multiplication
• LAPACK Users' Guide
• Exploiting fast matrix multiplication within the level 3 BLAS
• Triangular Factorization and Inversion by Fast Matrix Multiplication
• Accuracy and Stability of Numerical Algorithms
• Graph Expansion Analysis for Communication Costs of Fast Rectangular Matrix Multiplication
• Solving block low-rank linear systems by LU factorization is numerically stable
• Matrix Multiplication, a Little Faster
• Performance and Scalability of the Block Low-Rank Multifrontal Factorization on Multicore Architectures
• Improving Multifrontal Methods by Means of Block Low-Rank 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
• Nested Dissection of a Regular Finite Element Mesh