Research on fast and accurate verified numerical computations for large-scale systems of linear equations

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Solving systems of linear equations on computers is ubiquitous in scientific computing. Since numerical computations involve rounding errors, approximate solutions of the systems are obtained. Therefore, it is important to evaluate how accurate the approximate solutions are. In this research, methods of evaluating the accuracy of approximate solutions of large-scale systems of linear equations have been developed with introducing fast and accurate algorithms for calculating dot products, even if the solving problems are ill-conditioned.