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.
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U2 - 10.1088/1742-6596/1218/1/012014
DO - 10.1088/1742-6596/1218/1/012014
M3 - Conference article
AN - SCOPUS:85067825200
SN - 1742-6588
VL - 1218
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012014
T2 - 3rd International Conference on Mathematics; Pure, Applied and Computation, ICoMPAC 2018
Y2 - 20 October 2018
ER -