Bridging the Gap Between Flat and Hierarchical Low-Rank Matrix Formats: The Multilevel Block Low-Rank Format
From MaRDI portal
Publication:5376564
DOI10.1137/18M1182760zbMath1434.65051OpenAlexW2817952343MaRDI QIDQ5376564
Theo A. Mary, Alfredo Buttari, Patrick R. Amestoy, Jean-Yves L'Excellent
Publication date: 13 May 2019
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/18m1182760
Computational methods for sparse matrices (65F50) Factorization of matrices (15A23) Complexity and performance of numerical algorithms (65Y20) Numerical methods for low-rank matrix approximation; matrix compression (65F55)
Related Items
HODLR2D: A New Class of Hierarchical Matrices, Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations, Adjoint-state method for hybridizable discontinuous Galerkin discretization, application to the inverse acoustic wave problem, Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic, Sparse Approximate Multifrontal Factorization with Butterfly Compression for High-Frequency Wave Equations, Block Low-Rank Matrices with Shared Bases: Potential and Limitations of the BLR$^2$ Format, Recursive one-way Navier-Stokes equations with PSE-like cost
Uses Software
Cites Work
- Unnamed Item
- A direct solver with \(O(N)\) complexity for integral equations on one-dimensional domains
- Hierarchical matrices. A means to efficiently solve elliptic boundary value problems
- A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
- Construction and arithmetics of \(\mathcal H\)-matrices
- Introduction to hierarchical matrices with applications.
- A fast block low-rank dense solver with applications to finite-element matrices
- An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling
- Hierarchical Matrices: Algorithms and Analysis
- A fast, memory efficient and robust sparse preconditioner based on a multifrontal approach with applications to finite‐element matrices
- Fast algorithms for hierarchically semiseparable matrices
- Superfast Multifrontal Method for Large Structured Linear Systems of Equations
- The Multifrontal Solution of Indefinite Sparse Symmetric Linear
- The Multifrontal Method for Sparse Matrix Solution: Theory and Practice
- A Supernodal Approach to Sparse Partial Pivoting
- Improving Multifrontal Methods by Means of Block Low-Rank Representations
- A Fast $ULV$ Decomposition Solver for Hierarchically Semiseparable Representations
- Efficient Structured Multifrontal Factorization for General Large Sparse Matrices
- On the Complexity of the Block Low-Rank Multifrontal Factorization
- Nested Dissection of a Regular Finite Element Mesh
- Fast Hierarchical Solvers For Sparse Matrices Using Extended Sparsification and Low-Rank Approximation
