Introduction to Communication Avoiding Algorithms for Direct Methods of Factorization in Linear Algebra
| Autor: | Laura Grigori |
|---|---|
| Přispěvatelé: | Algorithms and parallel tools for integrated numerical simulations (ALPINES), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Mariano Mateos, Pedro Alonso |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Numerical linear algebra
Floating point Computation 010103 numerical & computational mathematics 0102 computer and information sciences computer.software_genre 01 natural sciences Algebra Computer engineering Factorization 010201 computation theory & mathematics Linear algebra Algorithm design 0101 mathematics [INFO.INFO-DC]Computer Science [cs]/Distributed Parallel and Cluster Computing [cs.DC] Focus (optics) Massively parallel computer [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] Mathematics |
| Zdroj: | SEMA SIMAI Springer Series Mariano Mateos; Pedro Alonso. SEMA SIMAI Springer Series, 13, Springer, pp.153-185, 2017, Computational Mathematics, Numerical Analysis and Applications, 978-3-319-49631-3. ⟨10.1007/978-3-319-49631-3_4⟩ Computational Mathematics, Numerical Analysis and Applications ISBN: 9783319496306 |
| DOI: | 10.1007/978-3-319-49631-3_4⟩ |
| Popis: | International audience; Modern, massively parallel computers play a fundamental role in a large and rapidly growing number of academic and industrial applications. However, extremely complex hardware architectures, which these computers feature, effectively prevent most of the existing algorithms to scale up to a large number of processors. Part of the reason behind this is the exponentially increasing divide between the time required to communicate a floating-point number between two processors and the time needed to perform a single floating point operation by one of the processors. Previous investigations have typically aimed at overlapping as much as possible communication with computation. While this is important, the improvement achieved by such an approach is not sufficient. The communication problem needs to be addressed also directly at the mathematical formulation and the algorithmic design level. This requires a shift in the way the numerical algorithms are devised, which now need to reduce, or even minimize when possible, the number of communication instances. Communication avoiding algorithms provide such a perspective on designing algorithms that minimize communication in numerical linear algebra. In this document we describe some of the novel numerical schemes employed by those communication avoiding algorithms, with a particular focus on direct methods of factorization. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|