Rchr

J-GLOBAL ID：200901073323647211 Update date: Jan. 31, 2024

NAKAO Mitsuhiro

ナカオミツヒロ | NAKAO Mitsuhiro

Affiliation and department：
Other affiliations (1)：

Waseda University Faculty of Science and Engineering Professor

Research field (2)： Applied mathematics and statistics , Basic mathematics

Research keywords (8)：解析学における計算機援用証明 , 偏微分方程式の解に対する数値的検証法 , 有限要素法の誤差解析 , 近似解の事後誤差評価 , 偏微分方程式の数値解法 , 精度保証付き数値計算 , 計算数学 , Computational Mathematics

Research theme for competitive and other funds (58)：

2021 - 2025 Computer-assisted solution verification for 3D flows with large Reynolds numbers
2021 - 2024 偏微分方程式の解に対する数値的検証法の新たな高度化の研究
2018 - 2022 Innovative research for self-validating numerical method of infinite dimensional problems
2015 - 2018 A study on the numerical verification method of solutions with high accuracy for the nonlinear mathematical models in infinite dimension
2012 - 2015 Numerical verification method of solutions for nonlinear evolutional equations

2012 - 2015 Optimal estimation for inverse of infinite-dimensional operator by self-validating numerical computations and its applications

2008 - 2011 Development of computer assisted analysis for complicated nonlinear phenomena

2007 - 2009 Foundation of high accuracy computational methods on the multiple-precision computer environment and its applications to analysi of inverse problems

2004 - 2008 Development and analysis of high-quality numerical methods and simulation for flow problems

2005 - 2007 Research of applied analysis toward the global theory for nonlinear systems

2005 - 2007 数値処理と数式処理の融合による計算機援用解析学の可能性に関する基礎的研究

2003 - 2006 Synthetic approach for the development of computer assisted analysis from the numerical verification methods

2002 - 2004 Applied Analysis for Nonlinear Systems

2002 - 2003 記号・代数計算による最適化問題解法と定理自動証明の研究

2001 - 2003 計算機による解析学創設の可能性に関する基礎的研究

2001 - 2003 Construction of Numerical Analysis for High-performance Large-Scale Computation

2001 - 2002 Synthetic approach for new developments of self-validating numerics

1999 - 2001 Construction of a Practical Computation Code for Heat Convection Problems with Slow Flow

1999 - 2001 Study on non-standard finite element approximation methods for partial differential equations

1999 - 2001 保存系の計算数理の総合的研究

1998 - 2000 Coordinative research on numerical analysis of complex systems and optimal control

1998 - 2000 Research on infinite precision numerical simulation of partial differential equations

1998 - 2000 Comprehensive Research Toward the Global Theory for the System of Nonlinear Partial Differential Equations

1998 - 2000 New Numerical Methods for Flow Problems and their Numerical Simulation

1997 - 2000 Development of practical methods for rigorous calculation with guaranteed accuracy

1997 - 2000 NONLINEAR STATISTICAL MODELING AND MODEL EVALUATION

1998 - 1999 計算機環境での理論的解析学遂行のための基礎研究

1998 - 1999 Self-validating numerics with applications to computational science and technology

1996 - 1998 Numerical Analysis of Evolution Systems

1996 - 1997 New Approaches to Scientific Computing and Applied Analysis

1996 - 1996 最適制御問題と最良近似問題の研究

1996 - 1996 Evaluation of Predictive Distributions based on Information and Entropy

1995 - 1996 Co-operative Research on Numerical Solutions in Seience and Technology

1995 - 1995 最適化と最良近似

1994 - 1995 Geometric study of linear differential equations in complex variables

1994 - 1994 関数方程式の解に対する精度保証付き数値計算法

1994 - 1994 多次元離散型データ解析のための正規直交化多次元スコア検定

1992 - 1994 Comprehensive Study on Fundamental and Applied Numerical Algorithms

1993 - 1993 非線形最適化の基礎理論とその応用

1993 - 1993 量子群・共形場・可解格子模型・ホロノミック q-差分系の相互理解

1992 - 1992 微分方程式に対する精度保証付き数値計算法

1992 - 1992 確率測度の無限次元級数解析と距離解析

1991 - 1992 Synthetical Researches on Applied Analysis and Computational Mathematics

1990 - 1992 ALL ROUND STUDY FOR THE NUMERICAL METHODS IN SCIENCE AND TECHNOLOGY

1990 - 1991 Computing Science and Complex systems

1990 - 1990 関数方程式に対する自己検証的数値計算法

1989 - 1989 無限次元の問題に対する数値計算法

1988 - 1988 力学系とその分岐の大域的、位相幾何学的研究

1987 - 1987 無限自由度の系における数理解析的研究

1986 - 1986 数理物理にあらわれる非線形偏微分方程式の数値解析的研究

数値計算結果の信頼性評価

精度保証付き数値計算

偏微分方程式の解に対する数値的検証法

偏微分方程式の数値解法

reliability in numerical computing

self-validating numerics

Numerical verification for the solutions of partial differential equations

Numerical solutions for partial differential equations

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Papers (71)：

Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao. Inclusion method of optimal constant with quadratic convergence for H01-projection error estimates and its applications. Journal of Computational and Applied Mathematics. 2023. 417. 114521-114521
Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao. Efficient Approaches for Verifying the Existence and Bound of Inverse of Linear Operators in Hilbert Spaces. JOURNAL OF SCIENTIFIC COMPUTING. 2023. 94. 2
Makoto Mizuguchi, Kouta Sekine, Kouji Hashimoto, Mitsuhiro T. Nakao, Shin’ichi Oishi. Rigorous numerical inclusion of the blow-up time for the Fujita-type equation. Japan Journal of Industrial and Applied Mathematics. 2022. 40. 1. 665-689
Takehiko Kinoshita, Yoshitaka Watanabe, Mitsuhiro T. Nakao. On Some Convergence Properties for Finite Element Approximations to the Inverse of Linear Elliptic Operators. Acta Cybernetica. 2022. 26. 1. 71-82
Xuefeng Liu, Mitsuhiro T. Nakao, Shin'ichi Oishi. Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains. Communications in Nonlinear Science and Numerical Simulation. 2022. 108

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MISC (90)：

木村拓馬, 皆本晃弥, 中尾充宏. 放物型方程式の全離散近似解に対するオーダー最良な構成的誤差評価について. 日本応用数理学会年会講演予稿集(CD-ROM). 2015. 2015. ROMBUNNO.9GATSU9NICHI,09:30,G,
Nakao Mitsuhiro T. Numerical verification method of solutions for nonlinear elliptic and evolutional problems (Mathematical Analysis of Viscous Incompressible Fluid). RIMS Kokyuroku. 2014. 1905. 112-131
木村拓馬, 木下武彦, 中尾充宏. [short invited paper]放物型問題の解の検証における計算上の注意. ハイパフォーマンスコンピューティングと計算科学シンポジウム論文集. 2013. 2013. 2013. 122-122
偏微分方程式の解に対する精度保証付き数値計算. 数学. 2013. 65. 113-132
Nakao Mitsuhiro. Reliability in numerical simulation(Review,<Special Feature>Reliability in numerical simulation). Journal of the Japan Society for Simulation Technology. 2012. 31. 3. 133-135

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Books (11)：

Numerical verification methods and computer-assisted proofs for partial differential equations
Springer 2019 ISBN:9789811376689
実例で学ぶ精度保証付き数値計算---理論と実装---
サイエンス社 2011
State of the Art for Self-Validating Numerical Computations, Special Issue of Japan Journal of Industrial and Applied Mathematics 26-2/3.
Kinokuniya, Tokyo 2009
偏微分方程式から数値シミュレーションへ/計算の信頼性評価, 現代技術への数学入門シリーズ
講談社 2008
Special Issue: Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004)
Journal of Computational and Applied Mathematics 199/2, Elsevier, 2007

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Education (4)：

1984 - 理学博士(九州大学)
1974 - 九州大学大学院理学研究科数学専攻修士課程修了
1972 - Kyushu University School of Sciences
1968 - 国立佐世保工業高等専門学校機械工学科卒業

Professional career (1)：

(BLANK) (Kyushu University)

Work history (13)：

2018/04 - 現在早稲田大学招聘研究員
2010/04 - 現在 Kyushu University Professor Emeritus
2016/12 - 2018/03 Waseda University Research Institute for Science and Engineering
2010/04 - 2016/03 National Institute of Technology, Sasebo College
2007/04 - 2010/03 九州大学産業技術数理研究センター長

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Committee career (8)：

2011 - 現在日本応用数理学会フェロー
2014 - 2022/03 科学技術振興機構 CREST 「現代の数理科学と連携するモデリング手法の構築」領域アドバイザー
2006 - 2017 日本学術会議連携会員
2008 - 2013 井上科学振興財団選考委員会委員
2008 - 2012 -: 日本数学会教育研究資金問題検討委員会委員

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Awards (6)：

2014/04 - Prizes for Science and Technology, Research Category, Ministry of Education, Culture, Sports, Science and Technology
2014/04 - 文部科学大臣表彰科学技術賞(研究部門)
2012/09 - Autumn Prize, The Mathematical Society of Japan
2012/09 - 日本数学会賞秋季賞
2011/09 - 日本応用数理学会論文賞(JJIAM部門)

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Association Membership(s) (3)：

情報処理学会 , 日本応用数理学会 , 日本数学会

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