The numerical computations with guaranteed accuracy called verified numerical computations are studied, herein. We focus on an accurate numerical solution for dense linear systems of the form Ax = b and error bound of in supercomputing, where is an approximate solution. First, we implemented accurate algorithms for a matrix-vector product for parallel and distributed computing, and then, applied them to iterative refinements. Next, we implemented verified numerical computations using the Parallel Basic Linear Algebra Subprograms (PBLAS) and the Scalable Linear Algebra Package library (ScaLAPACK). Numerical examples of the verified numerical computations for linear systems are presented using the Fujitsu FX100 supercomputer. They clearly illustrate the efficiency of the verified numerical computations.
|Journal||Journal of Physics: Conference Series|
|Publication status||Published - 2019 May 31|
|Event||3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018 - Surabaya, Indonesia|
Duration: 2018 Oct 20 → …
ASJC Scopus subject areas
- Physics and Astronomy(all)