Fast (Parallel) Dense Linear System Solvers in C-XSC Using Error Free Transformations and BLAS

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.

• Type: Conference
• Year: 2008
• Where: DAGSTUHL
• Authors: Walter Krämer, Michael Zimmer
• Keywords: DAGSTUHL 2008, Dense Linear, Exact Dot Products, Large Dense Systems, Software Engineering