AccessJP

Search

Menu

Study at TCU

Reseacher

Name AIHARA Kensuke
Official Title Associate Professor
Affiliation Department of Computer Science, Faculty of Information Technology
E-mail aiharak@tcu.ac.jp
Web
  1. http://www.comm.tcu.ac.jp/aiharak-sc/index_en.html
  2. http://www.risys.gl.tcu.ac.jp/Main.php?action=profile&type=detail&tchCd=5002026
Profile My specialty is numerical analysis in the fields of applied mathematics and computational science. In particular, I'm working on numerical linear algebra and its application to mathematical optimization.
The main subject of my research is to develop fast and accurate numerical algorithms for solving linear systems with matrices arising from various fields of scientific computing. I'm particularly interested in iterative solvers for large sparse linear systems and ill-conditioned least-squares problems that appear in numerical simulations to natural or physical phenomena. The aims of my studies are to develop novel and effective techniques that enhance the convergence, reduce the computational costs, and improve the accuracy of iterative methods, from both theoretical and experimental perspectives.
Moreover, I'm interested in optimization problems on Riemannian manifolds. My research also aims to develop effective Riemannian optimization algorithms that can be applied to statistical data analysis.
Research Field(Keyword & Summary)
  1. Computational science

    My research interests are the following:
    ・Iterative algorithms for solving large sparse linear systems
    ・Numerical methods for ill-conditioned least squares problems
    ・Application of numerical linear algebra to Riemannian optimization

  2. numerical analysis

    My research interests are the following:
    ・Iterative algorithms for solving large sparse linear systems
    ・Numerical methods for ill-conditioned least squares problems
    ・Application of numerical linear algebra to Riemannian optimization

  3. mathematical optimization

    My research interests are the following:
    ・Iterative algorithms for solving large sparse linear systems
    ・Numerical methods for ill-conditioned least squares problems
    ・Application of numerical linear algebra to Riemannian optimization
Representative Papers
  1. (1) Kensuke Aihara, GPBi-CGstab(L): A Lanczos-type product method unifying Bi-CGstab(L) and GPBi-CG, Numer. Linear Algebra Appl., 27 (2020), e2298.
  2. (2) Kensuke Aihara, Ryosuke Komeyama and Emiko Ishiwata, Variants of residual smoothing with a small residual gap, BIT, 59 (2019), pp.565--584.
  3. (3) Hiroyuki Sato and Kensuke Aihara, Cholesky QR-based retraction on the generalized Stiefel manifold, Comput. Optim. Appl., 72 (2019), pp.293--308.
  4. (4) Kensuke Aihara and Hiroyuki Sato, A matrix-free implementation of Riemannian Newton's method on the Stiefel manifold, Optim. Lett., 11 (2017), pp.1729--1741.
  5. (5) Kensuke Aihara, Variants of the groupwise update strategy for short-recurrence Krylov subspace methods, Numer. Algorithms, 75 (2017), pp.397--412.
  6. (6) Kensuke Aihara, Kuniyoshi Abe and Emiko Ishiwata, Preconditioned IDRStab Algorithms for Solving Nonsymmetric Linear Systems, IAENG Int. J. Appl. Math., 45 (2015), pp.164--174.
  7. (7) Kensuke Aihara, Kuniyoshi Abe and Emiko Ishiwata, A quasi-minimal residual variant of IDRstab using the residual smoothing technique, Appl. Math. Comput., 236 (2014), pp.67--77.
  8. (8) Kensuke Aihara, Kuniyoshi Abe and Emiko Ishiwata, A variant of IDRstab with reliable update strategies for solving sparse linear systems, J. Comput. Appl. Math., 259 (2014), pp.244--258.
Grant-in-Aid for Scientific Research Support: Japan Society for Promotion of Science (JSPS) https://nrid.nii.ac.jp/en/nrid/1000070735498/
Research Grants/Projects including subsidies, donations, grants, etc. Grant-in-Aid for Scientific Research (C), No.21K11925,
Principal Investigator, Japan Society for the Promotion of Science, 2021--2023.

Grant-in-Aid for Scientific Research (B), No.20H04195,
Co-Investigator, Japan Society for the Promotion of Science, 2020--2022.

Grant-in-Aid for Young Scientists, No.18K18064,
Principal Investigator, Japan Society for the Promotion of Science, 2018--2021.

Grant-in-Aid for Young Scientists (B), No.15K17498,
Principal Investigator, Japan Society for the Promotion of Science, 2015--2017.
Recruitment of research assistant(s) No
Affiliated academic society (Membership type) (1) The Japan Society for Industrial and Applied Mathematics (Rregular member)
(2) The Operations Research Society of Japan (Regular member)
Education Field (Undergraduate level) Basic Probability Theory and Statistics, Information Literacy , Programming, Numerical Analysis

Affiliation