iRRAM

The iRRAM: Exact Arithmetic in C++. The iRRAM is a very efficient C++ package for error-free real arithmetic based on the concept of a Real-RAM. Its capabilities range from ordinary arithmetic over trigonometric functions to linear algebra even with sparse matrices. We discuss the concepts and some highlights of the implementation.

Keywords for this software

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References in zbMATH (referenced in 36 articles )

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  1. Rösnick-Neugebauer, Carsten: Closed sets and operators thereon: representations, computability and complexity (2018)
  2. Brauße, Franz; Korovina, Margarita; Müller, Norbert: Using Taylor models in exact real arithmetic (2016)
  3. Brauße, Franz; Korovina, Margarita; Müller, Norbert Th.: Towards using exact real arithmetic for initial value problems (2016)
  4. Kawabata, Hideyuki; Iwasaki, Hideya: Improving floating-point numbers: a lazy approach to adaptive accuracy refinement for numerical computations (2016)
  5. Duracz, Jan; Farjudian, Amin; Konečný, Michal; Taha, Walid: Function interval arithmetic (2014)
  6. Hertling, Peter; Spandl, Christoph: Computing a solution of Feigenbaum’s functional equation in polynomial time (2014)
  7. Müller, Norbert; Ziegler, Martin: From calculus to algorithms without errors (2014)
  8. Sugiyama, Mahito; Hirowatari, Eiju; Tsuiki, Hideki; Yamamoto, Akihiro: Learning figures with the Hausdorff metric by fractals -- towards computable binary classification (2013)
  9. Lester, David R.: The world’s shortest correct exact real arithmetic program? (2012)
  10. Spandl, Christoph: Computational complexity of iterated maps on the interval (2012)
  11. Berger, Ulrich: From coinductive proofs to exact real arithmetic: theory and applications (2011)
  12. Farjudian, Amin: On the Kolmogorov complexity of continuous real functions (2011)
  13. Blass, Andreas; Dershowitz, Nachum; Gurevich, Yuri: Exact exploration and hanging algorithms (2010)
  14. Yu, Jihun; Yap, Chee; Du, Zilin; Pion, Sylvain; Brönnimann, Hervé: The design of Core 2: a library for exact numeric computation in geometry and algebra (2010)
  15. Bauer, Andrej; Kavkler, Iztok: A constructive theory of continuous domains suitable for implementation (2009)
  16. Bauer, Andrej; Taylor, Paul: The Dedekind reals in abstract Stone duality (2009)
  17. Bauer, Andrej; Kavkler, Iztok: Implementing real numbers with RZ (2008)
  18. Farjudian, Amin; Konečný, Michal: Time complexity and convergence analysis of domain theoretic Picard method (2008)
  19. Bauer, Andrej; Stone, Christopher A.: RZ: A tool for bringing constructive and computable mathematics closer to programming practice (2007)
  20. Gawronski, W.; Müller, J.; Reinhard, M.: Reduced cancellation in the evaluation of entire functions and applications to the error function (2007)

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