K. Tanaka

Ken'ichiro Tanaka (田中 健一郎)

Department of Mathematical and Computing Science,
School of Computing,
Institute of Science Tokyo (former Tokyo Institute of Technology)
2-12-1 Ookayama, Meguro-ku, Tokyo 152-8550 Japan
E-mail: kenichiro _at_ c.titech.ac.jp

Welcome to Ken'ichiro Tanaka's home page. I am a professor at Institute of Science Tokyo.

Research

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

Please see my research and publication list for more details.

My external pages:

News

[Oct. 24, 2024] I gave a talk entitled "On attempt for computation of general matrix functions by numerical integration" (in Japanese) in a conference held at Research Institute for Mathematical Sciences, Kyoto University.

[Oct. 18, 2024] A new paper "How Sharp Are Error Bounds? –Lower Bounds on Quadrature Worst-Case Errors for Analytic Functions–" has been published in SIAM Journal on Numerical Analysis. This is a paper corresponding to the preprint announced below on Jan. 17, 2024.

[Oct. 1, 2024] I have become a professor at Institute of Science Tokyo (former Tokyo Institute of Technology).

[Sep. 18, 2024] I gave a talk in the Second Workshop of JMCQMC -In Celebration of 50th Birthday of Prof. Josef Dick-. This workshop was organized by Prof. Takashi Goda, who invited me to it. My talk was concerned with the same content as what I presented in the annual conference of JSIAM four days ago.

[Sep. 16, 2024] From Sep. 14 to Sep. 16 in 2024, I participated in the annual conference of Japan Society of Industrial and Applied Mathematics (JSIAM) of AY2024, which was held at Kyoto University. In this conference, I gave a talk about our paper "How sharp are error bounds? ---lower bounds on quadrature worst-case errors for analytic functions---", which was accepted for publication in SIAM Journal on Numerical Analysis. Furthermore, Two of my master's graduate students gave talks about their work at this conference.

[May. 9, 2024] A new paper "Analysis of continuous dynamical system models with Hessians derived from optimization methods" (webpage) has been published. This paper is concerned with dynamical systems that correspond to optimization algorithms. The research of this paper was done in collaboration with several members of my laboratory.

[Jan. 17, 2024] My new preprint "How sharp are error bounds? ---lower bounds on quadrature worst-case errors for analytic functions---" (arXiv:2401.07196) has been published by a collaborative effort with Takashi Goda and Yoshihito Kazashi.
  In this preprint, we establish matching lower bounds for the worst-case errors of renowned numerical integration formulas on the real axis within the context of weighted Hardy spaces. Furthermore, we demonstrate the sharpness of their existing upper bounds.
  Considering the extensive reliance on one-dimensional integration as a subroutine in numerous scientific computing applications, our findings hold wide-ranging implications. They cater not only to experts in numerical integration but also extend to practitioners in the field.

[Jul. 21, 2023] I received an award for an excellent paper in Transactions of the JSIAM section in 2023, which was awarded by Japan Society for Industrial and Applied Mathematics. This is an award for the paper "Numerical Computation of Matrix Sign Function by Double Exponential Formula (二重指数関数型数値積分公式による行列符号関数の数値計算)", written in collaboration with Takahiro Nakaya, my former master's student. (webpage of the award) [Certificate of commendation]

[May. 19, 2023] Our book "Numerical Methods with Variable Transformations" (written in Japanese) has been published by Iwanami Shoten. This book is written in collaboration with Prof. Tomoaki Okayama. Here are its webpages: Japanese page, Translated page by Google.

[May. 5, 2023] The paper announced below has been published.

[Mar. 30, 2023] Our paper "Convergence analysis of approximation formulas for analytic functions via duality for potential energy minimization" (arXiv:1906.03133) has been accepted for publication in Japan Journal of Industrial and Applied Mathematics.

[Feb. 1, 2023] The paper announced below has been published.

[Jan. 12, 2023] The paper "Skeleton structure inherent in discrete-time quantum walks" (arXiv:2209.02943) has been accepted for publication in Physical Review A (notification).

[Jan. 12, 2023] The paper "Convergence rates for energies of interacting particles whose distribution spreads out as their number increases" (webpage) has been published.

[Sep. 17, 2022] I attended the 6th RIKEN-IMI-ISM-NUS-ZIB-MODAL-NHR Workshop on Advances in Classical and Quantum Algorithms for Optimization and Machine Learning. My co-author Mr. Tsuji gave a talk about "Pairwise Conditional Gradients without Swap Steps and Sparser Kernel Herding" in this workshop.

[Sep. 13, 2022] A preprint "Wavelet characterization of exponentially weighted Besov space with dominating mixed smoothness and its application to function approximation" (arXiv:2209.05396) has been released. This preprint was written in collaboration with my master's student Yoshihiro Kogure.

[Sep. 11, 2022] From September 8 to 10, I visited Hokkaido University in Sapporo to attend the Annual Meeting 2022 of the Japan Society for Applied Mathematics. This year's conference was held in a hybrid format.
Signboard of the meeting   A road in Hokkaido University

[Sep. 8, 2022] A preprint "Skeleton structure inherent in discrete-time quantum walks" (arXiv:2209.02943) has been released. This preprint is written by the same members as those of the proceedings in the previous news on Sep. 3.

[Sep. 3, 2022] On Aug. 20, our paper entitled "Skeleton structure inherent in quantum walks" was accepted for publication in the proceedings of the 2022 International Symposium on Nonlinear Theory and its Applications. This paper is written in collaboration with Mr. Tomoki Yamagami, Prof. Etsuo Segawa, Prof. Takatomo Mihana, Dr. André Röhm, Prof. Ryoichi Horisaki, and Prof. Makoto Naruse.

[Jul. 24, 2022] I visited Baltimore in the U.S. from Jul. 18 to Jul. 22 with Mr. Tsuji to attend ICML 2022 (The 39th International Conference on Machine Learning). We presented our paper "Pairwise Conditional Gradients without Swap Steps and Sparser Kernel Herding" at this conference. The title was slightly modified after the acceptance.
ICML 2022 opening   Inner Harbor

[Jun. 25, 2022] Our paper entitled "指数減衰する関数に対する全周波数領域におけるフーリエ変換の高精度な近似公式" (English translation: "Precise Approximation Formula for Fourier Transform of Functions with Exponential Decay for the Whole Frequency") has been published in Transactions of the Japan Society for Industrial and Applied Mathematics (webpage). This paper is written in collaboration with Mr. Naoya Takakura, my former student in the master's course.

[May 20, 2022] Our paper entitled "Yet another DE-Sinc indefinite integration formula" has been accepted for publication in Dolomites Research Notes on Approximation. This paper is written in collaboration with Prof. Tomoaki Okayama.

[May 20, 2022] The page ``research'' has been updated.

[May 15, 2022] Our paper entitled "Sparser Kernel Herding with Pairwise Conditional Gradients without Swap Steps" (arXiv:2110.12650) has been accepted for a presentation at ICML 2022 (The 39th International Conference on Machine Learning) (accepted papers). This paper is written in collaboration with Mr. Kazuma Tsuji and Prof. Sebastian Pokutta.

[May 5, 2022] This page has been renewed.

[Apr. 7, 2022] A new preprint entitled "Convergence rates for energies of interacting particles whose distribution spreads out as their number increases" (arXiv:2204.02672 ) has been released. This preprint is written in collaboration with Prof. Patrick van Meurs.

[Mar. 25, 2022] I was awarded the 2021 Best Teaching Award of the Faculty of Engineering. [Certificate]

[Dec. 28, 2021] Our paper entitled "Monte Carlo construction of cubature on Wiener space" (Journal page) has been published. This paper is written in collaboration with Mr. Satoshi Hayakawa, my former student in the master's course. He provided the main ideas in this work.

[Oct. 25, 2021] Our new preprint entitled "Sparser Kernel Herding with Pairwise Conditional Gradients without Swap Steps" (arXiv:2110.12650) has been released. This preprint is written in collaboration with Mr. Kazuma Tsuji and Prof. Sebastian Pokutta.

[Sep. 26, 2021] Our paper entitled "二重指数関数型数値積分公式による行列符号関数の数値計算" (English translation: "Numerical Computation of Matrix Sign Function by Double Exponential Formula") has been published in Transactions of the Japan Society for Industrial and Applied Mathematics. This paper is written in collaboration with Mr. Takahiro Nakaya, my former student in the master's course.

[May. 18, 2021] Our new preprint entitled "Acceleration of the kernel herding algorithm by improved gradient approximation" (arXiv:2105.07900) has been released. This preprint is written in collaboration with Mr. Kazuma Tsuji, my student in the master's course.

[May 1, 2021] My paper has been published as a book-chapter. Its title is "Construction of Approximation Formulas for Analytic Functions by Mathematical Optimization".

[Apr. 21, 2021] Our paper entitled "Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant" has been accepted for publication in Statistics and Computing. This paper is written in collaboration with Ms. Yici Chen, my former undergraduate student.

[Feb. 23, 2021] Our paper entitled "減衰度が指定された関数の近似に対する2つの公式の比較" (English translation: "Comparison of two formulas for approximating functions with a prescribed decay rate") has been accepted for publication in Transactions of the Japan Society for Industrial and Applied Mathematics. This paper is written in collaboration with Mr. Naoya Takakura, my student in the master's course.

[Feb. 23, 2021] My new preprint entitled "Kernel quadrature by applying a point-wise gradient descent method to discrete energies" (arXiv:2102.10887) has been released.

[Oct. 12, 2020] Our short paper entitled "Effective methods for obtaining good points for quadrature in reproducing kernel Hilbert spaces" has been published in JSIAM Letters. This is written in collaboration with one of my graduate students, Ryunosuke Oshiro.

[Sep. 11, 2020] I received an award for an excellent paper in JSIAM Letters section in 2020, which was awarded by Japan Society for Industrial and Applied Mathematics. This is an award for the paper "Improvement of the double exponential formula with conformal maps based on the locations of singularities", written in collaboration with Syunki Kyoya, my former undergraduate student. (webpage of the award) [Certificate of commendation]

[Aug. 20, 2020] Our new preprint entitled "Monte Carlo construction of cubature on Wiener space" (arXiv:2008.08219) has been released. This preprint is written in collaboration with Mr. Satoshi Hayakawa, my student in the master's course. He has provided the main ideas in this work.

[Aug. 5, 2020] I gave a talk entitled "Generation of point sets by global optimization for kernel-based numerical integration" in the special session "Probabilistic Numerical and Kernel-Based Methods" at Data-Centric Engineering Reading Group at The Alan Turing Institute, London, UK. This was an online session.

[Jul. 12, 2020] The paper entitled "Kernel-based interpolation at approximate Fekete points" has been published in Numerical Algorithms. This paper is written in collaboration with Dr. Toni Karvonen and Prof. Simo Sarkka.

[May. 1, 2020] A new preprint "Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant" (arXiv:2004.14660) has been released. This preprint is written in collaboration with Yici Chen, my former undergraduate student.

[Apr. 18, 2020] The paper entitled "Error bounds of potential theoretic numerical integration formulas in weighted Hardy spaces" has been published in JSIAM Letters. This paper is written in collaboration with Satoshi Hayakawa, my student in master's course.

Past News

News 2015-2019
News 2010-2014