A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures

@article{Buttari2009ACO,
  title={A Class of Parallel Tiled Linear Algebra Algorithms for Multicore Architectures},
  author={Alfredo Buttari and Julien Langou and Jakub Kurzak and Jack J. Dongarra},
  journal={Parallel Comput.},
  year={2009},
  volume={35},
  pages={38-53}
}

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References

SHOWING 1-10 OF 68 REFERENCES
Scheduling of QR Factorization Algorithms on SMP and Multi-Core Architectures
TLDR
This paper examines the scalable parallel implementation of the QR factorization of a general matrix, targeting SMP and multi-core architectures, and shows that the implementation effort is greatly simplified by expressing the algorithms in code with the FLAME/FLASH API, which allows matrices stored by blocks to be viewed and managed as matrices of matrix blocks.
Implementing Linear Algebra Routines on Multi-core Processors with Pipelining and a Look Ahead
TLDR
A pipelined model of parallel execution is presented, and the idea of look ahead is utilized in order to suppress the negative effects of sequential formulation of the algorithms.
Supermatrix out-of-order scheduling of matrix operations for SMP and multi-core architectures
TLDR
It is argued that traditional implementations of dense linear algebra matrix operations on SMP architectures cannot be easily modified to render high performance as well as scalability on these architectures, and the solution is to arrange the data structures and algorithms so that matrix blocks become the fundamental units of data.
Vector and parallel algorithms for Cholesky factorization on IBM 3090
  • R. AgarwalF. Gustavson
  • Computer Science
    Proceedings of the 1989 ACM/IEEE Conference on Supercomputing (Supercomputing '89)
  • 1989
TLDR
Various blocking schemes are described for vector and parallel implementation on 3090 VF and some of these algorithms have been included in the Engineering and Scientific Subroutine Library (ESSL).
Parallel Algorithms for Dense Linear Algebra Computations
TLDR
The purpose is to review the current status and to provide an overall perspective of parallel algorithms for solving dense, banded, or block-structured problems arising in the major areas of direct solution of linear systems, least squares computations, eigenvalue and singular value computation, and rapid elliptic solvers.
New Serial and Parallel Recursive QR Factorization Algorithms for SMP Systems
TLDR
A hybrid recursive algorithm that outperforms the LAPACK algorithm DGEQRF by 78% to 21% as m=n increases from 100 to 1000 and an automatic variable blocking that allow us to replace a level 2 part in a standard block algorithm by level 3 operations.
Parallel out-of-core computation and updating of the QR factorization
This article discusses the high-performance parallel implementation of the computation and updating of QR factorizations of dense matrices, including problems large enough to require out-of-core
Applying recursion to serial and parallel QR factorization leads to better performance
TLDR
A hybrid recursive algorithm that outperforms the LAPACK algorithm DGEQRF by about 20% for large square matrices and up to almost a factor of 3 for tall thin matrices is introduced.
Minimal Data Copy for Dense Linear Algebra Factorization
TLDR
A new result is described that shows that representing a matrix A as a collection of square blocks will reduce the amount of data reformating required by dense linear algebra factorization algorithms from O(n3) to O( n2).
QR Factorization for the CELL Processor
TLDR
It is demonstrated how the potential of the CELL processor can be utilized to the fullest by employing the new algorithmic approach and successfully exploiting the capabilities of theCELL processor in terms of Instruction Level Parallelism and Thread-Level Parallelism.
...
...