What do we need beyond IEEE arithmetic?
Computer arithmetic and self-validating numerical methods
ScaLAPACK user's guide
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Dense linear system: a parallel self-verified solver
International Journal of Parallel Programming
C-XSC and Closely Related Software Packages
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
Using C-XSC for high performance verified computing
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
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Existing selfverifying solvers for dense linear (interval-) systems in C-XSC provide high accuracy, but are rather slow. A new set of solvers is presented, which are a lot faster than the existing solvers, without losing too much accuracy. This is achieved through two main changes. First, an alternative method for the computation of exact dot products based on the DotK-Algorithm is implemented. Then, optimized BLAS and LAPACK routines are used for the most costly parts, in terms of runtime, of the algorithm. Verified results are achieved by manipulating the rounding mode of the processor. Finally, an efficient parallel version of these solvers for distributed memory systems, based on ScaLAPACK, is presented, which allows to solve very large dense systems. The new solver is compared to other solvers with respect to runtime and to numerical quality of the final result.