Verified numerical computations for large-scale linear systems

Katsuhisa Ozaki; Takeshi Terao; Takeshi Ogita; Takahiro Katagiri

Applications of Mathematics (2021)

  • Volume: 66, Issue: 2, page 269-285
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Ozaki, Katsuhisa, et al. "Verified numerical computations for large-scale linear systems." Applications of Mathematics 66.2 (2021): 269-285. <http://eudml.org/doc/297004>.

@article{Ozaki2021,
abstract = {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.},
author = {Ozaki, Katsuhisa, Terao, Takeshi, Ogita, Takeshi, Katagiri, Takahiro},
journal = {Applications of Mathematics},
keywords = {verified numerical computation; floating-point arithmetic; high-performance computing; large-scale linear system},
language = {eng},
number = {2},
pages = {269-285},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Verified numerical computations for large-scale linear systems},
url = {http://eudml.org/doc/297004},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Ozaki, Katsuhisa
AU - Terao, Takeshi
AU - Ogita, Takeshi
AU - Katagiri, Takahiro
TI - Verified numerical computations for large-scale linear systems
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 269
EP - 285
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.
LA - eng
KW - verified numerical computation; floating-point arithmetic; high-performance computing; large-scale linear system
UR - http://eudml.org/doc/297004
ER -

References

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