Book Chapter10.1007/978-3-540-75755-9_112
Optimizing a parallel self-verified method for solving linear systems
Mariana Kolberg,Lucas Baldo,Pedro Velho,Luiz Gustavo Fernandes,Dalcidio Moraes Claudio +4 more
- 18 Jun 2006
- pp 949-955
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TL;DR: This paper presents an optimization of a previously proposed parallel self-verified method for solving dense linear systems of equations, related to the way communication primitives were employed and to the identification of the points in the algorithm in which mathematical accuracy is needed to achieve reliable results.
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Abstract: Solvers for linear equation systems are commonly used in many different kinds of real applications, which deal with large matrices. Nevertheless, two key problems appear to limit the use of linear system solvers to a more extensive range of real applications: computing power and solution correctness. In a previous work, we proposed a method that employs high performance computing techniques together with verified computing techniques in order to eliminate the problems mentioned above. This paper presents an optimization of a previously proposed parallel self-verified method for solving dense linear systems of equations. Basically, improvements are related to the way communication primitives were employed and to the identification of the points in the algorithm in which mathematical accuracy is needed to achieve reliable results.
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Citations
Dense linear system: a parallel self-verified solver
TL;DR: A parallel self-verified solver for dense linear systems of equations using parallel computing techniques and the computation of the approximate inverse of matrix A and the preconditioning step is presented.
12
•Proceedings Article
A Multithreaded Verified Method for Solving Linear Systems in Dual-Core Processors
Mariana Kolberg,Daniel Cordeiro,Gerd Bohlender,Luiz Gustavo Fernandes,Alfredo Goldman +4 more
- 13 May 2008
TL;DR: This paper presents a new multithreaded approach for the problem of solving dense linear systems with verified results that allows the algorithm to run in a dual-core system without making any changes in the floating-point rounding mode used during the computations.
9
•Proceedings Article
Accurate sum and dot product with applications
Takeshi Ogita,Siegfried M. Rump,Shin'ichi Oishi +2 more
- 01 Jan 2004
TL;DR: This paper shows that the algorithms can be used to compute a very accurate inclusion of the solution of systems of linear equations.
8
Coupling from the past in hybrid models for file sharing peer to peer systems
Bruno Gaujal,Florence Perronnin +1 more
- 03 Apr 2007
TL;DR: This paper shows how file sharing peer to peer systems can be modeled by hybrid systems with a continuous parts corresponding to a fluid limit of files and a discrete part corresponding to customers, and shows that this hybrid system is amenable to perfect simulations.
7
Solving dense interval linear systems with verified computing on multicore architectures
Cleber Roberto Milani,Mariana Kolberg,Luiz Gustavo Fernandes +2 more
- 22 Jun 2010
TL;DR: This paper presents an ongoing research project which has the purpose of developing a self-verified solver for dense interval linear systems optimized for parallel execution on these new architectures.
5
References
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MPI: The Complete Reference
Marc Snir,Steve W. Otto,David W. Walker,Jack Dongarra,Steven Huss-Lederman +4 more
- 01 Jan 1996
TL;DR: MPI: The Complete Reference is an annotated manual for the latest 1.1 version of the standard that illuminates the more advanced and subtle features of MPI and covers such advanced issues in parallel computing and programming as true portability, deadlock, high-performance message passing, and libraries for distributed and parallel computing.
2.8K
INTLAB — INTerval LABoratory
Siegfried M. Rump
- 01 Jan 1999
TL;DR: INTLAB is a toolbox for Matlab supporting real and complex intervals, and vectors, full matrices and sparse matrices over those, designed to be very fast and achieves the anticipated speed with identical code on a variety of computers.
1.2K
•Journal Article
INTLAB - INTerval LABoratory.
TL;DR: INTLAB as mentioned in this paper is a toolbox for Matlab supporting real and complex intervals, and vectors, full matrices and sparse matrices over those, which is designed to be very fast.
963
Accurate Sum and Dot Product
TL;DR: Algorithms for summation and dot product of floating-point numbers are presented which are fast in terms of measured computing time and it is shown that the computed results are as accurate as if computed in twice or K-fold working precision.
443