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verified numerical computation; floating-point arithmetic; high-performance computing; large-scale linear system
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.
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