## Solving dense interval linear systems with verified computing on multicore architectures.(English)Zbl 1323.65137

Palma, José M. Laginha M. (ed.) et al., High performance computing for computational science – VECPAR 2010. 9th international conference, Berkeley, CA, USA, June 22–25, 2010. Revised selected papers. Berlin: Springer (ISBN 978-3-642-19327-9/pbk). Lecture Notes in Computer Science 6449, 435-448 (2011).
Summary: 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 $$15,000 \times 15,000$$ interval linear system on an eight core computer.
For the entire collection see [Zbl 1207.68016].

### MSC:

 65Y10 Numerical algorithms for specific classes of architectures 65F05 Direct numerical methods for linear systems and matrix inversion 65G20 Algorithms with automatic result verification 65G30 Interval and finite arithmetic 65Y05 Parallel numerical computation 65Y20 Complexity and performance of numerical algorithms

### Software:

C-XSC 2.0; LAPACK; ScaLAPACK; SuperMatrix; FLAME; C-XSC; MKL
Full Text: