Publications
Refereed: 16 (First/Corresponding: 10) International: 1
Preprint (3)
- Kazuaki Tanaka, Kohei Yatabe, Learn and Verify: A Framework for Rigorous Verification of Physics-Informed Neural Networks, (2025). arXiv
- Kazuaki Tanaka, Ryoga Iwanami, Kaname Matsue, Hiroyuki Ochiai, A Green's Function-Based Enclosure Framework for Poisson's Equation and Generalized Sub- and Super-Solutions, (2025). arXiv
- Sora Sawai, Kazuaki Tanaka, Katsuhisa Ozaki, Shin'ichi Oishi, Polygonal Sequence-driven Triangulation Validator: An Incremental Approach to 2D Triangulation Verification, (2024). arXiv
Refereed Papers (16)
- Ippei Obayashi, Shinya Miyajima, Kazuaki Tanaka, Koichi Mayumi, Enhanced Estimation Method for Partial Scattering Functions in CV-SANS via Gaussian Process with Prior Knowledge of Smoothness, Journal of Applied Crystallography, 58(3), 976-991, (2025). Journal Refereed
- Koichi Mayumi, Tatsuro Oda, Shinya Miyajima, Ippei Obayashi, Kazuaki Tanaka, Error evaluation of partial scattering functions obtained from contrast variation small-angle neutron scattering, Journal of Applied Crystallography, 58(1), 4-17, (2025). Journal Refereed
- Kazuaki Tanaka, Michael Plum, Kouta Sekine, Masahide Kashiwagi, Shin'ichi Oishi, Rigorous numerical enclosures for positive solutions of Lane-Emden's equation with sub-square exponents, Numerical Functional Analysis and Optimization, 43(3), 322-349, (2022). Journal arXiv Refereed Intl.
- Kazuaki Tanaka, Taisei Asai, A posteriori verification of the positivity of solutions to elliptic boundary value problems, Partial Differential Equations and Application, 3, 9, (2022). Journal Refereed
- Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi, Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems, Computers & Mathematics with Applications, 106, 18-26, (2022). Journal Refereed
- Taisei Asai, Kazuaki Tanaka, Shin'ichi Oishi, Numerical verification for asymmetric solutions of the Hénon equation on bounded domains, Journal of Computational and Applied Mathematics, 399, 113708, (2022). Journal Refereed
- Kazuaki Tanaka, A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations, Japan Journal of Industrial and Applied Mathematics, 38, 731-756, (2021). Journal Refereed
- 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, 7(1), 136-150, (2020). Journal Refereed
- Kazuaki Tanaka, Numerical verification method for positive solutions of elliptic problems, Journal of Computational and Applied Mathematics, 370, 112647, (2020). Journal arXiv Refereed
- 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, 29(1), 17-45, (2019). Journal Refereed
- Makoto Mizuguchi, Kazuaki Tanaka, Kouta Sekine, Shin'ichi Oishi, Estimation of Sobolev embedding constant on a domain dividable into bounded convex domains, Journal of Inequalities and Applications, 299, (2017). Journal Refereed
- Akitoshi Takayasu, Kaname Matsue, Takiko Sasaki, Kazuaki Tanaka, Makoto Mizuguchi, Shin'ichi Oishi, Numerical validation of blow-up solutions of ordinary differential equations, Journal of Computational and Applied Mathematics, 314, 10-29, (2017). Journal arXiv Refereed
- Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi, Sharp numerical inclusion of the best constant for embedding on bounded convex domain, Journal of Computational and Applied Mathematics, 311, 306-313, (2017). Journal arXiv Refereed
- Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi, Estimation of the Sobolev embedding constant on domains with minimally smooth boundary using extension operator, Journal of Inequalities and Applications, 389, (2015). Journal Refereed
- Kazuaki Tanaka, Kouta Sekine, Makoto Mizuguchi, Shin'ichi Oishi, Numerical verification of positiveness for solutions to semilinear elliptic problems, JSIAM Letters, 7, 73-76, (2015). Journal Refereed
- Kazuaki Tanaka, Akitoshi Takayasu, Xuefeng Liu, Shin'ichi Oishi, Verified norm estimation for the inverse of linear elliptic operators using eigenvalue evaluation, Japan Journal of Industrial and Applied Mathematics, 31, 665-679, (2014). Journal Refereed
Non-refereed Papers (2)
Proceedings (1)
- Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi, Computer assisted existence proof of solutions to system of partial differential equations with bounded convex polygonal domains, Proceedings of the Twenty-Eighth RAMP Symposium, (2016)
Review Articles (4)
- 田中一成, 未解決問題と対峙する／問いをつくり，問いに挑む, 数学セミナー 2025年12月号 通巻770号, (2025). Journal
- 眞弓皓一, 小田達郎, 宮島信也, 大林一平, 田中一成, 数理科学を活用したコントラスト変調小角散乱法による多成分有機ハイブリッド材料のナノ構造解析, 日本中性子科学会誌「波紋」Vol.35 No.4, 35(4), (2025)
- 田中一成, 精度保証付き数値計算の未来像－AI時代の計算機援用証明－, オペレーションズリサーチ 70巻6号, 70(6), (2025). Journal
- 田中一成, コンピュータも計算を間違う？－数値計算の精度と誤差－, 日本音響学会誌 78巻10号, 78(10), (2022). Journal