**Ken'ichiro Tanaka (田中 健一郎)**

**Department of Mathematical Informatics,**

Graduate School of Information Science and Technology,

University of Tokyo

Graduate School of Information Science and Technology,

University of Tokyo

7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656, Japan

E-mail: kenichiro (at) mist.i.u-tokyo.ac.jp

Welcome to Ken'ichiro Tanaka's home page. I am an associate professor of the University of Tokyo.

## Research

My research interest is in numerical analysis and computational methods in science and engineering.

- Function approximation, numerical integration, and their application to differential equations (in particular, double exponential (DE) Sinc methods)
- Numerical methods for economics and/or finance
- Mathematical optimization
- Numerical computation with guaranteed accuracy

Please see my research (to be updated) and publication list for more details.

My external pages:

## News

[Jan. 13, 2018] I submitted a new paper entitled "Design of accurate formulas for approximating functions in weighted Hardy spaces by discrete energy minimization" to an international journal. I wrote the paper in collaboration with Prof. Masaaki Sugihara.

[Dec.23, 2017] I gave a talk about designing approximation formulas by discrete energy minimization (in Japanese) at the workshop Workshop on Optimization: Foundations and Frontiers (WOO).

[Dec.15, 2017] I gave a talk about designing approximation formulas by discrete energy minimization (in Japanese) at the workshop Interaction between Pure and Applied Mathematics 2017 (IPA Math 2017).

[Nov.12, 2017] On Nov.10, 2017, I gave a talk entitled "Design of accurate numerical integration formulas in weighted Hardy spaces" (in Japanese) at the RIMS conference "The State of the Art in Numerical Analysis: Theory, Methods, and Applications".

[Aug.13, 2017] Our paper entitled "Potential Theoretic Approach to Design of Accurate Numerical Integration Formulas in Weighted Hardy Spaces" has been published as a chapter of the book Approximation Theory XV: San Antonio 2016 (Springer). This is a conference paper based on my talk at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas.

[Apr. 3, 2017] On April 1, 2017, I became an associate professor at Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo.

[Mar. 31, 2017] The paper "A function approximation formula using the Ganelius sampling points（Ganelius標本点を用いた関数近似公式）" (written in Japanese) was published on Mar. 25, 2017 in the Transactions of the Japan Society for Industrial and Applied Mathematics（日本応用数理学会論文誌）. I wrote this paper in collaboration with Takashi Ushima, Tomoaki Okayama, and Masaaki Sugihara.

[Feb. 20, 2017] My article entitled "Mathematics of numerical integration (数値積分法の数理)" has been published in the March 2017 issue of "Daigaku eno Sugaku (大学への数学)", a monthly journal for candidates for universities published by Tokyo shuppan (東京出版).

[Dec. 14, 2016] The paper "A function approximation formula using the Ganelius sampling points" (written in Japanese) has been accepted for publication in Transactions of the Japan Society for Industrial and Applied Mathematics (See the news on Jul. 4, 2016 below).

[Nov. 28, 2016] I submitted a new paper entitled "Potential theoretic approach to design of accurate numerical integration formulas in weighted Hardy spaces" to proceedings of an international conference. I wrote the paper in collaboration with Tomoaki Okayama and Masaaki Sugihara.

[Nov. 25, 2016] I gave a talk about the design of accurate formulas for function approximation and numerical integration on weighted Hardy spaces in Iwate Mathematical Science Seminar.

[Oct. 21, 2016] I submitted a new paper entitled "An optimal approximation formula for functions with singularities" (arXiv:1610.06844) to a journal. I wrote the paper in collaboration with Tomoaki Okayama and Masaaki Sugihara.

[Sep. 12, 2016] I gave a talk about the design of accurate formulas for numerical integration on weighted Hardy spaces in JSIAM annual meeting 2016.

[Jul. 4, 2016] I submitted a new paper entitled "A function approximation formula using the Ganelius sampling points" written in Japanese to a journal. I wrote the paper in collaboration with Takashi Ushima, Tomoaki Okayama, and Masaaki Sugihara.

[Jun. 21, 2016] I gave a talk about the potential theoretic approach to approximation of functions in the East Asia SIAM Conference (EASIAM 2016) in Macao, Macao SAR.

[Jun. 16, 2016] Our paper "Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces"(with Dr. Tomoaki Okayama and Prof. Masaaki Sugihara) has been published in the IMA Journal of Numerical Analysis (see also the news on Apr. 5, 2016 below).

[May. 23, 2016] I gave a talk about the potential theoretic approach to approximation of functions in 15th International Conference on Approximation Theory (AT15) in San Antonio, TX, USA.

[May. 9, 2016]
I gave a talk about the potential theoretic approach to approximation of functions and definite integrals in
UTNAS (University of Tokyo Numerical Analysis Seminar) **#079 (2016-3)** (in Japanese).

[Apr. 5, 2016] Our paper "Potential theoretic approach to design of accurate formulas for function approximation in symmetric weighted Hardy spaces"(with Dr. Tomoaki Okayama and Prof. Masaaki Sugihara) has been accepted for publication in the IMA Journal of Numerical Analysis.

[Mar. 16, 2016]
My paper entitled "Design of highly accurate formulas for numerical integration in weighted Hardy spaces with the aid of potential theory" (written in Japanese) was published in **the Bulletin of Musashino University Musashino Center of Mathematical Engineering (No.1)** on Mar. 1, 2016. This is the first issue of the bulletin published by Musashino Center of Mathematical Engineering (MCME).

[Feb. 10, 2016] I attended a conference jointly held by Musashino Univ., Meiji Univ., and Ryukoku Univ. on "mathematical engineering", "mathematical sciences based on modeling and analysis", and "mathematical analysis" at Seta campus of Ryukoku Univ. I gave a talk about the potential theoretic approach to function approximation.

[Jan. 19, 2016] I attended the second international ACCA-JP/UK Workshop (ACCA = Applied and Computational Complex Analysis) on January 18 and 19, 2016 at Kyoto University. In this workshop I gave a talk about the potential theoretic approach to function approximation, the full details of which is written in the preprint arXiv:1511.04530 released on Nov. 17, 2015 as mentioned below.

[Nov. 17, 2015] My collaborators and I have released a new preprint entitled "Potential theoretic approach to design of highly accurate formulas for function approximation in weighted Hardy spaces" (arXiv:1511.04530). In this preprint, we have proposed a new framework for designing accurate formulas for approximation of functions using potential theory.

[Sep. 16, 2015] The paper "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis", written by Dr. Alexis Akira Toda and myself, has been published in the SIAM Journal on Numerical Analysis (Here is the page of the article).

[Aug. 27, 2015] On Aug. 25, 2015, I gave a talk entitled "Potential theoretic approach to design an optimal formula for function approximation in a weighted Hardy space" in the conference NEW DIRECTIONS IN NUMERICAL COMPUTATION, IN CELEBRATION OF NICK TREFETHEN'S 60TH BIRTHDAY.

[Aug. 15, 2015] I participated in the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015) at Beijing, China, from Aug. 10 to 14, 2015. In this congress, I gave a talk about the contents of my paper published recently in the IMA Journal of Numerical Analysis (see the news on Jul. 23, 2015 below).

[Aug. 4, 2015] The paper "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis" (arXiv:1308.3753), written by Dr. Alexis Akira Toda and myself, is accepted for publication in the SIAM Journal on Numerical Analysis.

[Jul. 24, 2015] I gave a talk about a potential theoretic approach for unified design of function approximation formulas in weighted Hardy spaces in the conference "Recent developments in numerical analysis with special emphasis on complex analysis".

[Jul. 23, 2015] My paper "A fast and accurate numerical method for the symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula" is published online in the IMA Journal of Numerical Analysis.

[Jun. 20, 2015] My paper "A fast and accurate numerical method for the symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula" (arXiv:1408.0157) is accepted for publication in the IMA Journal of Numerical Analysis.

[Jun. 17, 2015] On Jun 8, 2015, I gave a talk about "Designing an optimal interpolation formula on a weighted Hardy space using potential theory" (in Japanese) in NAS 2015 (the 44th Numerical Analysis Symposium) at Katsunuma-budo-kyo (in Yamanashi prefecture).

[Apr. 11, 2015] I gave a talk about "Designing an optimal interpolation formula on a weighted Hardy space using potential theory" (in Japanese) in Prof. Murota's 60th anniversary symposium "Tradition and trend of mathematical engineering".

[Apr. 10, 2015] On April 1, 2015, I became an associate professor at Department of Mathematical Engineering, Faculty of Engineering, Musashino University.

[Feb. 03, 2015] A preprint "Discretizing Distributions with Exact Moments: Error Estimate and Convergence Analysis" is released. This is a revision of the preprint "Error Estimate and Convergence Analysis of Moment-Preserving Discrete Approximations of Continuous Distributions" available on arXiv:1308.3753.

[Jan. 13, 2015] A paper "A new method of convergence acceleration of series expansion for analytic functions in the complex domain" was published online. It is available here.

[Dec. 23, 2014] The day before yesterday, a paper "A new method of convergence acceleration of series expansion for analytic functions in the complex domain" was accepted for publication in Japan Journal of Industrial and Applied Mathematics. This is a joint work with Prof. Sunao Murashige (see List of Coauthors).

[Dec. 23, 2014] On Dec. 18, 2014, I read my paper "A fast and accurate numerical method for symmetric Lévy processes" （対称Lévy過程に対する高速高精度数値計算法） at "Joint conference of applied mathematics 2014" （2014年度 応用数学合同研究集会）. This paper is a condensed written summary of the preprint arXiv:1408.0157 released on Aug. 01, 2014 as written below.

[Dec. 12, 2014] A few days ago, an article "Error estimate and convergence analysis of moment-preserving discrete approximations of continuous distributions" was published in AIP conference proceedings. This article is available on this site.

[Aug. 25, 2014] This page is renewed.

[Aug. 01, 2014] A new preprint "A fast and accurate numerical method for the symmetric Lévy processes based on the Fourier transform and sinc-Gauss sampling formula" is released in arXiv:1408.0157. In this preprint, I have proposed a numerical method for the Kolmogorov forward equations of Lévy processes.