A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
LAPACK++: a design overview of object-oriented extensions for high performance linear algebra
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
ScaLAPACK user's guide
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
MPI: The Complete Reference
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
C++ Toolbox for Verified Scientific Computing I: Basic Numerical Problems
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
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
Parallel Solutions of Large Dense Linear Systems Using MPI
PARELEC '02 Proceedings of the International Conference on Parallel Computing in Electrical Engineering
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
A Test Matrix Collection for Non-Hermitian Eigenvalue Problems
SIAM Journal on Scientific Computing
Optimizing a parallel self-verified method for solving linear systems
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in scientific computing
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
Comments on fast and exact accumulation of products
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
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A parallel version of the self-verified method for solving linear systems was presented in [20, 21]. In this research we propose improvements aiming at a better performance. The idea is to implement an algorithm that uses technologies as MPI communication primitives associated to libraries as LAPACK, BLAS and C-XSC, aiming to provide both self-verification and speed-up at the same time. The algorithms should find an enclosure even for ill-conditioned problems. In this scenario, a parallel version of a self-verified solver for dense linear systems appears to be essential in order to solve bigger problems. Moreover, the major goal of this research is to provide a free, fast, reliable and accurate solver for dense linear systems.