日本語
Hiroshima City University 
Graduate School of Information Sciences 
Dept. of Systems Engineering 

Lecturer 
Okayama Tomoaki 

My website is here.  

Career
Part-Time Assistant Professor, Toho University  2005/04-2005/09 
Part-Time Teacher, Fuchunishi High School  2005/04-2006/03 
Part-Time Lecturer, Yachiyo Rehabilitation College  2007/04-2009/03 
Research Fellow DC2, Japan Society for the Promotion of Science  2009/04/01-2010/03/31 
Project Lecturer, Graduate School of Economics, Hitotsubashi University  2010/04/01-2014/03/31 
Lecturer, Graduate School of Information Sciences, Hiroshima City University  2014/04/01-Present 

Academic background
The University of Tokyo  Faculty of Engineering  Department of Mathematical Engineering and Information Physics  2005/03/25  Graduated 
The University of Tokyo  Graduate School of Information Science and Technology  Department of Mathematical Informatics  Master course  2007/03/22  Completed 
The University of Tokyo  Graduate School of Information Science and Technology  Department of Mathematical Informatics  Doctor course  2010/03/24  Completed 

Academic degrees
Ph.D. (Information Science and Technology)  The University of Tokyo  2010/03/24 

Licenses and qualifications
High School Teacher, 1st Grade, Mathematics  2005/03/31 
High School Teacher, 1st Grade, Information  2005/03/31 

Research Areas
Computational science 
Foundations of mathematics/Applied mathematics 

Research keywords
Numerical Analysis 

Research Funds
Grant-in-Aid from Ministry of Education, Science, Sports, and Culture  Reformulation and expanding application of the Sinc methods  2017/04/01-Present  Representative 
Grant-in-Aid from Ministry of Education, Science, Sports, and Culture  Development of super high-efficient methods for equations with singularity and their theoretical supports  2012/04/01-2017/03/31  Representative 
Grant-in-Aid from Ministry of Education, Science, Sports, and Culture  Research toward the practical use of Sinc numerical methods based on theoretical analysis  2010/04/01-2012/03/31  Representative 
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Bibliography
Calculus for students in the science and engineering majors  Toshiyuki KATSURA (ed.), Yoshiaki OKAZAKI, Tomoaki OKAYAMA, Natsuo SAITO, Yoshihisa SATO, Makoto TAGAMI, Masayuki HIROKADO, Hideo HIROSE  Section 5 "Derivative of functions of several variables" 104-128  Baifukan  2017/02/28  978-4-563-01209-0  本書は,理工系の学生が,無理なく微分積分学を学習できるよう配慮してまとめられた教科書である.数学の完成された理論をただ理路整然と解説するというのではなく,初心者が間違いやすい点については誤った使用例をあげるなどして注意を喚起し,本質的な理解をするための助けとなるような書き方がなされている.とくに特徴があるのは演習問題による学習法である.IRT(項目反応理論)を利用したWeb演習システム(通称「愛あるって」)が採用され,学習者の到達レベルにあわせた問題を提供し,それに従って問題を解いていくことにより自然に学力が向上するよう配慮されている. 
Handbook of Applied Mathematics  Junkichi SATSUMA, Shin'ichi OISHI and Masaaki SUGIHARA (eds.)  "Function Approximation" in Scientific Computation and Numerical Analysis 384-387  Asakura Publishing  2013/11/15  978-4-254-11141-5  数値解析,行列・固有値問題の解法,計算の品質,微分方程式の数値解法,数式処理,最適化,ウェーブレット,カオス,複雑ネットワーク,神経回路と数理脳科学,可積分系,折紙工学,数理医学,数理政治学,数理設計,情報セキュリティ,数理ファイナンス,離散システム,弾性体力学の数理,破壊力学の数理,機械学習,流体力学,自動車産業と応用数理,計算幾何学,数論アルゴリズム,数理生物学,逆問題,などの30分野から260の重要な用語について2~4頁で解説したハンドブックである. 
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Papers
Research paper (scientific journal)  Only  Theoretical analysis of a Sinc-Nyström method for Volterra integro-differential equations and its improvement  Tomoaki OKAYAMA  Applied Mathematics and Computation  Elsevier B.V.  324, 1-15  2018/05/01  10.1016/j.amc.2017.11.062  A Sinc-Nyström method for Volterra integro-differential equations was developed by Zarebnia (2010). The method is quite efficient in the sense that exponential convergence can be obtained even if the given problem has endpoint singularity. However, its exponential convergence has not been proved theoretically. In addition, to implement the method, the regularity of the solution is required, although the solution is an unknown function in practice. This paper reinforces the method by presenting two theoretical results: (1) the regularity of the solution is analyzed, and (2) its convergence rate is rigorously analyzed. Moreover, this paper improves the method so that a much higher convergence rate can be attained, and theoretical results similar to those listed above are provided. Numerical comparisons are also provided. 
Research paper (scientific journal)  Only  Theoretical analysis of Sinc-collocation methods and Sinc-Nyström methods for systems of initial value problems  Tomoaki OKAYAMA  BIT Numerical Mathematics  Springer Netherlands  58/ 1, 199-220  2018/03  10.1007/s10543-017-0663-z  A Sinc-collocation method was proposed by Stenger, who also gave a theoretical analysis of the method in the case of a ``scalar'' equation. This paper extends the theoretical results to the case of a ``system'' of equations. Furthermore, this paper proposes a more efficient method by replacing the variable transformation employed in Stenger's method. The efficiency was confirmed by both a theoretical analysis and some numerical experiments. In addition to the existing and newly proposed Sinc-collocation methods, this paper also gives similar theoretical results for the Sinc-Nyström methods proposed by Nurmuhammad et al. In terms of computational cost, the newly proposed Sinc-collocation method is the most efficient among these methods. 
Research paper (scientific journal)  Only  Error estimates with explicit constants for the Sinc approximation over infinite intervals  Tomoaki OKAYAMA  Applied Mathematics and Computation  Elsevier B.V.  319, 125-137  2018/02/15  10.1016/j.amc.2017.02.022  The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined with a proper variable transformation. The convergence rate has been analyzed for typical cases including finite, semi-infinite, and infinite intervals. Recently, for verified numerical computations, a more explicit, “computable” error bound has been given in the case of a finite interval. In this paper, such explicit error bounds are derived for other cases. 
Research paper (international conference proceedings)  Joint  Explicit error bound for Muhammad-Mori's SE-Sinc indefinite integration formula over the semi-infinite interval  Ryota HARA and Tomoaki OKAYAMA  Proceedings of the 2017 International Symposium on Nonlinear Theory and its Applications  677-680  2017/12  In this paper, we consider two numerical integration formulas over the semi-infinite interval. First, Stenger proposed a formula by means of the Sinc indefinite integration and a single-exponential (SE) transformation. Second, Muhammad--Mori proposed another formula by replacing the SE transformation in Stenger's formula. An error bound of Stenger's formula has been already given. However, any error bound of Muhammad--Mori's formula has not yet been given. In this study, we give an error bound for Muhammad--Mori's formula, and compare the two formulas. 
Research paper (international conference proceedings)  Joint  Potential theoretic approach to design of accurate numerical integration formulas in weighted Hardy spaces  Ken'ichiro TANAKA, Tomoaki OKAYAMA and Masaaki SUGIHARA  Approximation Theory XV: San Antonio 2016  Springer, Cham  335-360  2017/07  10.1007/978-3-319-59912-0_17  We propose a method for designing accurate numerical integration formulas on weighted Hardy spaces, which are regarded as spaces of transformed integrands by some useful variable transformations such as the double-exponential transformation. We begin with formulating an optimality of numerical integration formulas in the space by using the norms of the error operators corresponding to those formulas. Then, we derive an expression of the minimum value of the norms, which gives a criterion for an optimal sequence of sampling points for numerical integration. Based on the expression, we propose an algorithm designing accurate numerical integration formulas on the space by a potential theoretic approach. The effectiveness of the designed formulas is supported by some numerical examples. 
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Research presentations
Oral presentation(general)  Error analysis of Sinc-Nyström methods for initial value problems of ordinary differential equations  The 47th Numerical Analysis Symposium 2018 (NAS2018)  2018/06/08 
Oral presentation(general)  Improvement of the SE formula for infinite integrals of unilateral rapidly decreasing functions and its theoretical error estimate  JSIAM 2018 Meeting of the Union of Research Activity Groups  2018/03/16 
Oral presentation(general)  Improvement of the DE-Sinc-Nyström method for initial value problems of ordinary differential equations  JSIAM 2018 Meeting of the Union of Research Activity Groups  2018/03/15 
Oral presentation(general)  Explicit error bound for Muhammad-Mori's SE-Sinc indefinite integration formula over the semi-infinite interval  The 2017 International Symposium on Nonlinear Theory and its Applications  2017/12/07 
Oral presentation(general)  Verified algorithm for the gamma function using double exponential formula and its applications  The 36th JSST Annual International Conference on Simulation Technology  2017/10/26 
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Prizes
Paper Award in 2013, The Japan Society for Industrial and Applied Mathematics  2013/09 
Talk Award in 2007, The Japan Society for Industrial and Applied Mathematics  2008/04 
Paper Award in 2007, The Japan Society for Industrial and Applied Mathematics  2007/09 
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Allotted class
Analysis I 
Linear Algebra I 
Exercises in Linear Algebra I 
Analysis II 
Numerical Methods 
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Textbooks and teaching materials
Calculus for students in the science and engineering majors  2017/02/28  本書は,理工系の学生が,無理なく微分積分学を学習できるよう配慮してまとめられた教科書である.数学の完成された理論をただ理路整然と解説するというのではなく,初心者が間違いやすい点については誤った使用例をあげるなどして注意を喚起し,本質的な理解をするための助けとなるような書き方がなされている.とくに特徴があるのは演習問題による学習法である.IRT(項目反応理論)を利用したWeb演習システム(通称「愛あるって」)が採用され,学習者の到達レベルにあわせた問題を提供し,それに従って問題を解いていくことにより自然に学力が向上するよう配慮されている. 
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Social activities
Lecture at Kamo senior high school: Numerical methods for computers ---Technique for approximating a solution---  2017/07/06-2017/07/06 
Lecture at Ishigaki junior high school: Road to a university faculty position  2014/06/11-2014/06/11 
Three JSIAM Research Activity Groups Cooperative Seminar on "Applied Mathematics"  2012/12/25-2012/12/25 
Seminar at Manabi Pia 21: Introduction to block-building  2012/02/12-2012/02/12 
Seminar at the University of Tokyo: Introduction to commutators  2011/09/04-2011/09/04 
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Memberships of academic societies
Mathematical Society of Japan  2016/10-Present 
Mathematics Education Society in Japan  2014-Present 
The Japan Society for Industrial and Applied Mathematics  2006/04-Present 
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Committee Career
The Japan Society for Industrial and Applied Mathematics (JSIAM)  Vice-Chief Editor, Transactions of JSIAM  2018/04-Present 
The Japan Society for Industrial and Applied Mathematics (JSIAM)  Secretary Editor, Transactions of JSIAM  2017/04-2018/03 
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