\(\mathcal H\)-LU factorization on many-core systems

DOI10.1007/s00791-014-0226-7zbMath1388.65210OpenAlexW2088536107MaRDI QIDQ1685030

Ronald Kriemann

Publication date: 13 December 2017

Published in: Computing and Visualization in Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00791-014-0226-7

zbMATH Keywords

parallel algorithmshierarchical matricesmany-core processorsDAG-based

Mathematics Subject Classification ID

Analysis of algorithms (68W40) Parallel algorithms in computer science (68W10) Parallel numerical computation (65Y05) Complexity and performance of numerical algorithms (65Y20) Direct numerical methods for linear systems and matrix inversion (65F05)

Related Items

Survey on the technique of hierarchical matrices, SemiAutomatic Task Graph Construction for $\mathcal{H}$-Matrix Arithmetic, Distributed-memory hierarchical interpolative factorization, \(\mathcal H\)-FAINV: hierarchically factored approximate inverse preconditioners, Algorithmic patterns for \(\mathcal {H}\)-matrices on many-core processors, Parallel Solution of Hierarchical Symmetric Positive Definite Linear Systems, Domain decomposition methods in scattered data interpolation with conditionally positive definite radial basis functions, Parallel accelerated cyclic reduction preconditioner for three-dimensional elliptic PDEs with variable coefficients, An Efficient Multicore Implementation of a Novel HSS-Structured Multifrontal Solver Using Randomized Sampling, $\mathcal{H}$-Matrix Based Second Moment Analysis for Rough Random Fields and Finite Element Discretizations

Uses Software

• LAPACK
• CUDA
• OpenCL
• MAGMA
• PLASMA
• HSL_MA87

Cites Work

• Parallel \(\mathcal H\)-matrix arithmetics on shared memory systems
• A sparse matrix arithmetic based on \({\mathfrak H}\)-matrices. I: Introduction to \({\mathfrak H}\)-matrices
• Construction and arithmetics of \(\mathcal H\)-matrices
• Performance Of H-Lu Preconditioning For Sparse Matrices
• The Multifrontal Solution of Indefinite Sparse Symmetric Linear
• LAPACK Users' Guide
• Design of a Multicore Sparse Cholesky Factorization Using DAGs
• Parallel black box $$\mathcal {H}$$ -LU preconditioning for elliptic boundary value problems