<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We present a prototype task-parallel algorithm for the solution of hierarchical symmetric positive definite linear systems via the <italic>ℋ</italic>-Cholesky factorization that builds upon the parallel programming standards and associated runtimes for OpenMP and OmpSs. In contrast with previous efforts, our proposal decouples the numerical aspects of the linear algebra operation from the complexities associated with high performance computing. Our experiments make an exhaustive analysis of the efficiency attained by different parallelization approaches that exploit either task-parallelism or loop-parallelism via a runtime. Alternatively, we also evaluate a solution that leverages multi-threaded parallelism via the parallel implementation of the Basic Linear Algebra Subroutines (BLAS) in Intel MKL.</p></abstract>

We present a prototype task-parallel algorithm for the solution of hierarchical symmetric positive definite linear systems via the ℋ-Cholesky factorization that builds upon the parallel programming standards and associated runtimes for OpenMP and OmpSs. In contrast with previous efforts, our proposal decouples the numerical aspects of the linear algebra operation from the complexities associated with high performance computing. Our experiments make an exhaustive analysis of the efficiency attained by different parallelization approaches that exploit either task-parallelism or loop-parallelism via a runtime. Alternatively, we also evaluate a solution that leverages multi-threaded parallelism via the parallel implementation of the Basic Linear Algebra Subroutines (BLAS) in Intel MKL.

Parallel Solution of Hierarchical Symmetric Positive Definite Linear Systems

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Parallel Solution of Hierarchical Symmetric Positive Definite Linear Systems"}

We present a prototype task-parallel algorithm for the solution of hierarchical symmetric positive definite linear systems via the ℋ-Cholesky factorization...

Parallel Solution of Hierarchical Symmetric Positive Definite Linear Systems

Published Online: Jun 22, 2017

Page range: 201 - 212

Received: Mar 06, 2017

Accepted: Jun 22, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00017

Keywords
Hierarchical matrices, hierarchical arithmetic, Cholesky factorization, high performance, multicore processors

© 2017 José I. Aliaga, Rocío Carratalá-Sáez, Enrique S. Quintana-Ortí, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Parallel Solution of Hierarchical Symmetric Positive Definite Linear Systems

Published Online: Jun 22, 2017

Page range: 201 - 212

Received: Mar 06, 2017

Accepted: Jun 22, 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00017

KeywordsHierarchical matrices, hierarchical arithmetic, Cholesky factorization, high performance, multicore processors

© 2017 José I. Aliaga, Rocío Carratalá-Sáez, Enrique S. Quintana-Ortí, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Hierarchical matrices, hierarchical arithmetic, Cholesky factorization, high performance, multicore processors