Programming with POSIX threads
Programming with POSIX threads
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
FLAME: Formal Linear Algebra Methods Environment
ACM Transactions on Mathematical Software (TOMS)
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
SuperMatrix: a multithreaded runtime scheduling system for algorithms-by-blocks
Proceedings of the 13th ACM SIGPLAN Symposium on Principles and practice of parallel programming
Parallel Verified Linear System Solver for Uncertain Input Data
SBAC-PAD '08 Proceedings of the 2008 20th International Symposium on Computer Architecture and High Performance Computing
High Performance Computing for Computational Science - VECPAR 2008
Dense linear system: a parallel self-verified solver
International Journal of Parallel Programming
The impact of multicore on math software
PARA'06 Proceedings of the 8th international conference on Applied parallel computing: state of the art in 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
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Automatic result verification is an important tool to reduce the impact of floating-point errors in numerical computation and to guarantee the mathematical rigor of results. One fundamental problem in Verified Computing is to find an enclosure that surely contains the exact result of a linear system. Many works have been developed to optimize Verified Computing algorithms using parallel programming techniques and message passing paradigm on clusters of computers. However, the High Performance Computing scenario changed considerably with the emergence of multicore architectures in the past few years. 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. The current version has obtained up to 85% of reduction at execution time and a speedup of 6.70 when solving a 15,000 × 15,000 interval linear system on an eight core computer.