kvライブラリに関連した論文、記事など

1. Neil Hoffman, Kazuhiro Ichihara, Masahide Kashiwagi, Hidetoshi Masai, Shin'ichi Oishi, Akitoshi Takayasu: Verified Computations for Hyperbolic 3-Manifolds, Experimental Mathematics, Volume 25, Issue 1, pp. 66-78, 2016.
   (arXiv)
   (web site)
   kvライブラリが公開される前のソースコードが使用されている。
2. 松本翔太, 別納健市, 増田健太, 上田和紀: 制約に基づいたパラメトリックハイブリッドシステムの精度保証シミュレーション, 2017年度人工知能学会全国大会（第31回）
3. 松本 翔太, 上田 和紀: パラメタを含むハイブリッドシステムに対するアフィン演算を用いた記号シミュレーション, 日本ソフトウェア科学会第33回大会 (2016年度) 講演論文集
4. 増田 健太, 上田 和紀: ハイブリッド制約言語HydLaにおける非線形常微分方程式の表現とその記号付き精度保証計算, 2018年度人工知能学会全国大会（第32回）
5. 酒井将大, 田中一成, 大石進一: 半線形楕円型境界値問題の精度保証付き数値計算結果の改善, 日本応用数理学会論文誌, Vol. 29, No. 1, 2019, pp. 17--45.
6. B. G.-Tóth, L. G. Casado, E. M. T. Hendrix, F. Messine: On new methods to construct lower bounds in simplicial branch and bound based on interval arithmetic, Journal of Global Optimization volume 80, pages 779–804 (2021)
7. Hiroki Takizawa, Junichi Iwakiri, Kiyoshi Asai: RintC: fast and accuracy-aware decomposition of distributions of RNA secondary structures with extended logsumexp, BMC Bioinformatics volume 21, Article number: 210 (2020)
8. Shinya Uchiumi: Guaranteed bounds for the eigenvalues of Laplacian in curved domains, Numerical methods for spectral problems: theory and applications, 2-4 September, 2019, RIMS, Kyoto, Japan
9. 薮智仁 石井大輔: Why3を用いた区間演算ライブラリの検証, 日本ソフトウェア科学会第 34 回大会 (2017 年度) 講演論文集
10. 村上 椋星, 薮 智仁, 石井 大輔: Why3を用いた区間べき関数のプログラム検証, 日本ソフトウェア科学会第 36 回大会 (2019 年度) 講演論文集
11. 中山 大輔: 拡張affine演算を用いた精度保証計算ライブラリ, 電気通信大学2017年度修士論文
    (software)
12. 松田望, 山本野人, 中山大輔: 二次形式を用いたAffine演算の拡張について, 第47回数値解析シンポジウム (NAS2018)
13. 寺坂 元: 非双曲型平衡点近傍における局所 Lyapunov 関数の精度保証による構成 電気通信大学2018年度修士論文
14. Naoya Yamanaka, Tomoaki Okayama, Shin’ichi Oishi: Verified Error Bounds for the Real Gamma Function Using Double Exponential Formula over Semi-infinite Interval, International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015: Mathematical Aspects of Computer and Information Sciences, pp. 224-228
15. 近藤祐史, 大墨礼子, 村尾裕一, 齋藤友克: 3変数陰関数描画の実装について, 数式処理 Bulletin of JSSAC(2017), Vol. 23, No. 1, pp. 20-29
16. Tomasz Kapela, Marian Mrozek, Daniel Wilczak, Piotr Zgliczynski: CAPD::DynSys: A flexible C++ toolbox for rigorous numerical analysis of dynamical systems, Communications in Nonlinear Science and Numerical Simulation, Volume 101, October 2021, 105578
    (author's copy)
17. Jan Bouwe van den Berg, Ray Sheombarsing: Rigorous numerics for ODEs using Chebyshev series and domain decomposition, Journal of Computational Dynamics, 2021, 8 (3) : 353-401.
18. 関根晃太: 偏微分方程式の解の計算機援用存在証明法のためのC++を用いた精度保証付き数値計算ライブラリの構築, 第59回プログラミング・シンポジウム
19. Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi: Numerical verification methods for a system of elliptic PDEs, and their software library, Nonlinear Theory and Its Applications, IEICE, vol. 12, no. 1, pp. 41–74
20. James Paul Turner, Thomas Nowotny: Arpra: An Arbitrary Precision Range Analysis Library, Frontiers in Nuroinfomatics, 25 June 2021
21. Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi: Numerical verification of positiveness for solutions to semilinear elliptic problems, JSIAM Letters, 2015 Volume 7 Pages 73-76
22. Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi: Sharp numerical inclusion of the best constant for embedding \(H_{0}^{1}(\Omega)\hookrightarrow L^{p}(\Omega)\) on bounded convex domain, Journal of Computational and Applied Mathematics, Vol.311, pp.306–313, Feb., 2017.
23. Kazuaki Tanaka: A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations, Japan Journal of Industrial and Applied Mathematics volume 38, pages 731–756 (2021)
24. Taisei Asai, Kazuaki Tanaka, Shin’ichi Oishi: Numerical verification for asymmetric solutions of the Henon equation on bounded domains, Journal of Computational and Applied Mathematics, Volume 399, 1 January 2022, 113708
25. Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi: A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator, Numerische Mathematik volume 146, pages 907–926 (2020)
26. Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi, Masahide Kashiwagi: A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems, Applied Numerical Mathematics, Volume 169, November 2021, Pages 87-107
27. Kaname Matsue, Akitoshi Takayasu: Numerical validation of blow-up solutions with quasi-homogeneous compactifications, Numerische Mathematik volume 145, pages 605–654 (2020)
28. Kaname Matsue, Akitoshi Takayasu: Rigorous numerics of blow-up solutions for ODEs with exponential nonlinearity, Journal of Computational and Applied Mathematics, Volume 374, 15 August 2020, 112607
29. Kaname Matsue: Rigorous numerics of tubular, conic, star-shaped neighborhoods of slow manifolds for fast-slow systems, arXiv
30. 松江 要: Fast-slow系における精度保証付き数値計算, 数学, 2019 年 71 巻 3 号 p. 252-281
31. 桂田 祐史: 「現象と数学」数値計算法の数理 --- 精度保証付き数値計算入門 ---
32. Tomasz Kapela, Daniel Wilczak, Piotr Zgliczynski: Recent advances in rigorous computation of Poincare maps, arXiv
    ( author's copy )
33. Marko Lange, Siegfried M. Rump: Faithfully Rounded Floating-point Computations, ACM Transactions on Mathematical Software, Volume 46, Issue 3, September 2020, Article No.: 21, pp. 1–20
34. Joao Rivera, Franz Franchetti, Markus Puschel: An Interval Compiler for Sound Floating-Point Computations, 2021 IEEE/ACM International Symposium on Code Generation and Optimization (CGO)
    (author's copy)
    (software)
    dd区間演算を実装している?
35. Ekaterina Auer, Wolfram Luther: RECOMMENDER TECHNIQUES FOR SOFTWARE WITH RESULT VERIFICATION, Eccomas Proceedia UNCECOMP (2019) 509-533
36. 松江 要: 書評「精度保証付き数値計算の基礎」
37. よーる: 完全精度 expf 関数の作り方
38. よーる: IntelのFast Adder (FADD)について
39. MMNMM_259: 誤差ジャッジ問題のw/t作業をするときのためのTIPS
40. Arnd Hartmanns: Correct Probabilistic Model Checking with Floating-Point Arithmetic, Tools and Algorithms for the Construction and Analysis of Systems: 28th International Conference, TACAS 2022, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022, Munich, Germany, April 2–7, 2022
41. José Fernández and Bogláka G.-Tóth: Interval Tools in Branch-and-Bound Methods for Global Optimization, The Palgrave Handbook of Operations Research, pp 237–267, Springer, 2022.
42. Yuta Matsushima, Kazuaki Tanaka, Shin'ichi Oishi: Numerical verification for positive solutions of Allen–Cahn equation using sub- and super-solution method, Journal of Advanced Simulation in Science and Engineering, Volume 7, Issue 1, pp. 136-150, 2020.
43. Jan Bouwe van den Berg and Ray Sheombarsing: Rigorous numerics for ODEs using Chebyshev series and domain decomposition, Journal of Computational Dynamics, 8(3), pp.353-401 (2021).
44. 松江 要: Fast-slow系における精度保証付き数値計算, 数学, 71巻3号, pp.252-281 (2019年7月)
45. Kaname Matsue: Rigorous numerics for fast-slow systems, Sugaku Expositions 36, pp.221-253 (2023)
46. Shin'ichi Oishi, Kouta Sekine: Inclusion of periodic solutions for forced delay differential equation modeling El Niño, Nonlinear Theory and Its Applications, IEICE, vol. 12, no. 3, pp.575-610 (2021)
47. 田中 佑奈, 小林 領, 大石 進一: 複合ガウス・ルジャンドル求積法と直積型公式に基づく精度保証付き数値重積分法, 日本応用数理学会論文誌, 31, 4, pp.197-221 (2021).
48. Yuanyuan Yang, XinYu Lyu, Sida He, Xiliang Lu, Ji Qi, Zhihao Li: On the robustness of double-word addition algorithms, arXiv
49. 中野 夏樹, 関根 晃太, 大石 進一: 外力項を加えた池田遅延微分方程式における分数調波解の精度保証付き数値計算, 日本応用数理学会論文誌, 33, 4, pp.132-148 (2022).
50. kv (swMATH ID: 31712 Software Authors: Masahide Kashiwagi)
51. @shocker-0x15: アフィン演算で求める三角形上の関数の範囲
52. Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi: Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems, Computers and Mathematics with Applications, 106, pp.18-26 (2022).