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https://hdl.handle.net/1822/23671
Título: | Blocked schur algorithms for computing the matrix square root |
Autor(es): | Deadman, Edvin Higham, Nicholas J. Ralha, Rui |
Palavras-chave: | Matrix square roots BLAS3 Parallel computing |
Data: | 2013 |
Editora: | Springer |
Revista: | Lecture Notes in Computer Science |
Resumo(s): | The Schur method for computing a matrix square root reduces the matrix to Schur triangular form and then computes a square root of the triangular matrix. We show that by using either a standard blocking or recursive blocking the computation of the square root of the triangular matrix can be made rich in matrix multiplication. Numerical experiments making appropriate use of level 3 BLAS show significant speedups over the point algorithm, both in the square root phase and in the algorithm as a whole. In parallel implemetnations, recursive blocking is found to provide better performance than standard blocking when parallelism comes only from threaded BLAS, but the reverse is true when parallelism is explicitly expressed using OpenMP. The excellent numerical stability of the point algorithm is shown to be preserved by blocking. These results are extended to the real Schur method. Blocking is also shown to be effective for multiplying triangular matrices. |
Tipo: | Artigo em ata de conferência |
Descrição: | Applied Parallel and Scientific Computing: 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 2012, Revised Selected Papers. |
URI: | https://hdl.handle.net/1822/23671 |
ISBN: | 978-3-642-36802-8 |
DOI: | 10.1007/978-3-642-36803-5_12 |
ISSN: | 0302-9743 |
Versão da editora: | The original publication is available at www.springerlink.com |
Arbitragem científica: | yes |
Acesso: | Acesso aberto |
Aparece nas coleções: |
Ficheiros deste registo:
Ficheiro | Descrição | Tamanho | Formato | |
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edvin_nick_rui.pdf | 275,25 kB | Adobe PDF | Ver/Abrir |