A cooperative conjugate gradient method for linear systems permitting efficient multi-thread implementation
Bhaya, Amit; Bliman, Pierre-Alexandre; Niedu, Guilherme; Pazos, Fernando
O documento é disponibilizado pela fonte de origem, que mantém a versão integral e as condições de uso.
Resumo
This paper revisits, in a multi-thread context, the so-called multi-parameter or block conjugate gradient (B-CG)methods, first proposed as sequential algorithms by O’Leary and Brezinski, for the solution of the linear system Ax = b, for an n-dimensional symmetric positive definite matrix A. Instead of the scalar parameters of the classical CG algorithm, which minimizes a scalar functional at each iteration, multiple descent and conjugate directions are updated simultaneously. Implementation involves the use of multiple threads and the algorithm is referred to as cooperative CG (CCG) to emphasize that each thread now uses information that comes from the other threads. It is shown that for a sufficiently large matrix dimension n, the use of an optimal number of threads results in a worst case flop count of O(n7/3) in exact arithmetic. Numerical experiments on a multi-core, multi-thread computer, for synthetic and real matrices, illustrate the theoretical results
Ficha do documento
- Tipo
- Artigo científico
- Ano
- 2018
- Instituição
- Springer
- Fonte
- Repositório da FGV
- Idioma
- Inglês
- Acesso
- Não informado
- Identificador
- oai:repositorio.fgv.br:10438/28064
Conteúdos relacionados
- Artigo científicoCooperative concurrent asynchronous computation of the solution of symmetric linear systemsSpringer · 2017
- DissertaçãoAnálise teórica do método de reflexão circuncentrada no problema de viabilidade convexa convexo-afimFundação Getulio Vargas · 2026
- LivroInterval observers for SIR epidemic models subject to uncertain seasonalitySpringer Verlag · 2017
- OutroInterval observer for SIR epidemic model subject to uncertain seasonalityEMAp - Escola de Matemática Aplicada · 2016
