What do we need beyond IEEE arithmetic?
Computer arithmetic and self-validating numerical methods
MPI: The Complete Reference
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C-XSC: A C++ Class Library for Extended Scientific Computing
C-XSC: A C++ Class Library for Extended Scientific Computing
SIAM Journal on Scientific Computing
High Performance Computing for Computational Science - VECPAR 2008
Solving dense interval linear systems with verified computing on multicore architectures
VECPAR'10 Proceedings of the 9th international conference on High performance computing for computational science
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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.