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 (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. 
Research paper (scientific journal)  Joint  Error estimate with explicit constants for the trapezoidal formula combined with Muhammad-Mori's SE transformation for the semi-infinite interval  Tomoaki OKAYAMA and Koichi MACHIDA  JSIAM Letters  The Japan Society for Industrial and Applied Mathematics  9, 45-47  2017/05/26  10.14495/jsiaml.9.45  An efficient quadrature formula, known as the Single-Exponential (SE) formula, was proposed by Stenger for the definite integral of an exponentially decaying function over the semi-infinite interval. The formula was derived by combining the trapezoidal formula with a SE transformation. An error bound of the formula was already given. In this study, we investigate another SE formula obtained by replacing the transformation with Muhammad-Mori's SE transformation. Its error bound was determined by theoretical analysis. Numerical comparisons of Stenger's SE formula with that of Muhammad-Mori's are given as well. 
Research paper (scientific journal)  Joint  Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces  Ken'ichiro TANAKA, Tomoaki OKAYAMA and Masaaki SUGIHARA  IMA Journal of Numerical Analysis  Oxford University Press  37/ 2, 861-904  2017/04  10.1093/imanum/drw022  We propose a method for designing accurate interpolation formulas on the real axis for function approximation in weighted Hardy spaces. Examples of interpolation formulas for functions in such spaces include the SE-Sinc and DE-Sinc formulas, which are very accurate owing to the accuracy of sinc interpolation in the weighted Hardy spaces with single-exponential (SE) and double-exponential (DE) weights w, respectively. However, it is not guaranteed that the sinc formulas are optimal in weighted Hardy spaces, although Sugihara has demonstrated that they are near optimal. An explicit form for an optimal approximation formula has only been given in weighted Hardy spaces with SE weights of a certain type. In general cases, explicit forms for optimal formulas have not been provided so far. We adopt a potential theoretic approach to obtain almost optimal formulas in weighted Hardy spaces in the case of general weight functions w. We formulate the problem of designing an optimal formula in each space as an optimization problem written in terms of a Green potential with an external field. By solving the optimization problem numerically, we obtain an almost optimal formula in each space. 
Research paper (scientific journal)  Joint  A function approximation formula using the Ganelius sampling points  Takashi USHIMA, Ken'ichiro TANAKA, Tomoaki OKAYAMA and Masaaki SUGIHARA  Transactions of the Japan Society for Industrial and Applied Mathematics  The Japan Society for Industrial and Applied Mathematics  27/ 1, 1-20  2017/03/25  10.11540/jsiamt.27.1_1  In this paper we give a function approximation formula using the Ganelius sampling points for analytic functions with end-point singularities. Then we show that it is more accurate than the SE-Sinc formula and that it is optimal. 
Research paper (other science council materials etc.)  Joint  高等学校の統計分野における基本的な用語の定義の差異について  Teruo TANAKA, Manabu SATO, Natsuo SAITO, Mitsuhiro SEKINE, Masayuki HIROKADO, Tomoaki OKAYAMA  2017年度数学教育学会春季年会予稿集  Mathematics Education Society of Japan  224-226  2017/03/25  高等学校における現行の教育課程から「データの分析」を含む「数学Ⅰ」が必履修となり,統計分野が重要視されている.特に,データと変量は重要な用語である.本稿では,「数学Ⅰ」と「数学B」において教科書によってこれらの用語の定義に差異があることを示す.そして,高等学校学習指導要領における記述も踏まえつつ,統計学の立場からこれらの定義の比較と考察を行う.さらに,統計分野を指導する際の留意点を述べる. 
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Research presentations
Oral presentation(general)  Improvement of the SE-Sinc-Nyström method for initial value problems of ordinary differential equations  The 2017 Annual Meeting of JSIAM  2017/09/08 
Oral presentation(general)  Improvement of the SE-Sinc approximation with boundary treatment over the semi-infinite interval and its error estimate  The 2017 Annual Meeting of JSIAM  2017/09/06 
Poster presentation  Verified error bounds for the gamma function using double exponential formula  International Workshop on Industrial Mathematics / ICIAM Board Meeting 2017  2017/05/18 
Oral presentation(invited, special)  Verified error bounds for the modified Bessel function of the second kind using double exponential formula over semi-infinite interval  International Workshop on Numerical Verification and its Applications 2017  2017/03/18 
Oral presentation(invited, special)  Recent development of variable transformations combined with the trapezoidal formula  International Workshop on Numerical Verification and its Applications 2017  2017/03/18 
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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)  Manager of Editorial Board, Transactions of JSIAM  2017/04-Present 
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