TY - JOUR
T1 - Verified Numerical Computations for Large-Scale Linear Systems
AU - Ozaki, Katsuhisa
AU - Terao, Takeshi
AU - Ogita, Takeshi
AU - Katagiri, Takahiro
N1 - Funding Information:
This research was supported by MEXT as “Exploratory Challenge on Post-K computer” (Development of verified numerical computations and super high-performance computing environment for extreme researches) using computational resources of the K computer at RIKEN R-CCS and Fujitsu FX100 at Nagoya University through the HPCI System Research Project (Project ID: hp190192). Acknowledgments
Publisher Copyright:
© 2021, Institute of Mathematics, Czech Academy of Sciences.
PY - 2021/4
Y1 - 2021/4
N2 - This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical solutions. We report the implementation of a verification method for large-scale linear systems and some numerical results using the RIKEN K computer and the Fujitsu PRIMEHPC FX100, which show the high performance of the verified numerical computations.
AB - This paper concerns accuracy-guaranteed numerical computations for linear systems. Due to the rapid progress of supercomputers, the treatable problem size is getting larger. The larger the problem size, the more rounding errors in floating-point arithmetic can accumulate in general, and the more inaccurate numerical solutions are obtained. Therefore, it is important to verify the accuracy of numerical solutions. Verified numerical computations are used to produce error bounds on numerical solutions. We report the implementation of a verification method for large-scale linear systems and some numerical results using the RIKEN K computer and the Fujitsu PRIMEHPC FX100, which show the high performance of the verified numerical computations.
KW - 65G20
KW - 65G50
KW - 65Y05
KW - floating-point arithmetic
KW - high-performance computing
KW - large-scale linear system
KW - verified numerical computation
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U2 - 10.21136/AM.2021.0318-19
DO - 10.21136/AM.2021.0318-19
M3 - Article
AN - SCOPUS:85101197906
SN - 0862-7940
VL - 66
SP - 269
EP - 285
JO - Applications of Mathematics
JF - Applications of Mathematics
IS - 2
ER -