Abstract
Double-double and Quad-double arithmetics are effective tools to reduce the round-off errors in floating-point arithmetic. However, the dense data structure for high-precision numbers in MuPAT/Scilab requires large amounts of memory and a great deal of the computation time. We implemented sparse data types ddsp and qdsp for double-double and quad-double numbers. We showed that sparse data structure for high-precision arithmetic is practically useful for solving a system of ill-conditioned linear equation to improve the convergence and obtain the accurate result in smaller computation time.
Tsubasa Saito and Satoko Kikkawa were at Tokyo University of Science while conducting this research.
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The authors would like to thank the reviewers for their helpful comments.
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Saito, T., Kikkawa, S., Ishiwata, E., Hasegawa, H. (2014). Effectiveness of Sparse Data Structure for Double-Double and Quad-Double Arithmetics. In: Wyrzykowski, R., Dongarra, J., Karczewski, K., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2013. Lecture Notes in Computer Science(), vol 8384. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55224-3_60
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DOI: https://doi.org/10.1007/978-3-642-55224-3_60
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