Rchr
J-GLOBAL ID：200901073323647211
Update date: Nov. 11, 2024
NAKAO Mitsuhiro
ナカオ ミツヒロ | NAKAO Mitsuhiro
Affiliation and department：
Other affiliations (1)：
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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 (75)：
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Takehiko Kinoshita, Yoshitaka Watanabe, Nobito Yamamoto, Mitsuhiro T. Nakao. Inclusion method of optimal constant with quadratic convergence for $H_0^1$-projection error estimates and its applications. Journal of Computational and Applied Mathematics. 2023. 417. 114521-114521
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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
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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
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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
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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
ｍore...
MISC (94)：
Books (11)：
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Numerical verification methods and computer-assisted proofs for partial differential equations
Springer 2019 ISBN:9789811376689
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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
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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
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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
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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
- 2009/05 - Kyushu University
- 2003/08 - 2008/03 21世紀COEプログラム「機能数理学の構築と展開」拠点リーダー
- 2002/07 - 2006/07 Kyushu University Faculty of Mathematics
- 1994/06 - 九州大学教授(大学院数理学研究科, 2000年4 月より数理学研究院)
- 1988/10 - Kyushu University
- 1982/04 - 九州工業大学講師(工学部), 1984 年10 月同助教授
- 1980/01 - Kyushu University
- 1974/04 - 日本電信電話公社(現NTT)横須賀電気通信研究所研究員
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Committee career (8)：
Awards (6)：
Association Membership(s) (3)：
情報処理学会
, 日本応用数理学会
, 日本数学会
