What do we need beyond IEEE arithmetic?
Computer arithmetic and self-validating numerical methods
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
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
Fast (Parallel) Dense Linear System Solvers in C-XSC Using Error Free Transformations and BLAS
Numerical Validation in Current Hardware Architectures
A Note on Solving Problem 7 of the SIAM 100-Digit Challenge Using C-XSC
Numerical Validation in Current Hardware Architectures
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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This article presents a parallel self-verified solver for dense linear systems of equations. This kind of solver is 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: solution correctness and high computational cost. In order to solve the first one, verified computing would be an interesting choice. An algorithm that uses this concept is able to find a highly accurate and automatically verified result providing more reliability. However, the performance of these algorithms quickly becomes a drawback. Aiming at a better performance, parallel computing techniques were employed. Two main parts of this method were parallelized: the computation of the approximate inverse of matrix A and the preconditioning step. The results obtained show that these optimizations increase significantly the overall performance.