TY - JOUR

T1 - Verified numerical computations for dense linear systems in supercomputing

AU - Ozaki, Katsuhisa

N1 - Funding Information:
This research is supported by the project: Development of Verified Numerical Computations and Super High-performance Computing Environment for Extreme Researches, Ministry of Education, Culture, Sports, Science and Technology. We express our sincere thanks to the Information Technology Center of Nagoya University. The function flib omp fesetround is developed by Fujitsu.
Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2019/5/31

Y1 - 2019/5/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85067825200&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067825200&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1218/1/012014

DO - 10.1088/1742-6596/1218/1/012014

M3 - Conference article

AN - SCOPUS:85067825200

VL - 1218

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012014

T2 - 3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018

Y2 - 20 October 2018

ER -