Ken Hayami

Profile Information

Affiliation: (Professor Emeritus), National Institute of Informatics
: (Professor Emeritus), The Graduate University for Advanced Studies (SOKENDAI)

Degree: Ph.D.(Jun, 1991, Wessex Institute of Technology, and Council for National Academic Awards, U.K.)
Ph.D. (Engineering)(Feb, 1993, The University of Tokyo)

Contact information: hayaminii.ac.jp
Other name(s) (e.g. nickname): Ken
Researcher number: 20251358
J-GLOBAL ID: 200901050210481180
researchmap Member ID: 1000201876

External link: http://research.nii.ac.jp/~hayami/index-e.html

I am doing research and teaching on the theory and application of numerical computation. Emphasis is on the mathematical analysis of numerical algorithms and the development of new algorithms.
Main areas of my present research interests are numerical linear algebra (iterative solution of linear systems, least squares problems, constrained and nonlinear least squares problems) and its application to optimization, inverse problems, and ill-posed problems.

Research Interests

Research Areas

Research History

Jun, 2023 - Present

President, Japan Society for Industrial and Applied Mathematics (JSIAM)
Apr, 2021 - Present

Professor Emeritus, The Graduate University for Advanced Studies
Apr, 2021 - Present

Professor Emeritus, National Institute of Informatics
Jun, 2018 - Present

Fellow, Japan Society for Industrial and Applied Mathematics (JSIAM)
Apr, 2006 - Mar, 2021

Professor, Principles of Informatics Research Division, National Institute of Informatics
Apr, 2004 - Mar, 2021

Professor, Department of Informatics, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies
Apr, 2006 - Mar, 2008

Head, Department of Informatics, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies
Jan, 2001 - Mar, 2006

Professor, Mathematical Informatics, Foundations of Informatics Research Division, National Institute of Informatics
Apr, 2002 - Mar, 2004

Professor, Department of Informatics, School of Mathematical and Physical Science, The Graduate University for Advanced Studies
Apr, 1995 - Dec, 2000

Associate Professor, Department of Mathematical Engineering and Information Physics, Graduate School of Engineering, The University of Tokyo
Apr, 1993 - Dec, 2000

Associate Professor, Department of Mathematical Engineering and Information Physics, Faculty of Engineering, The University of Tokyo
Apr, 1997 - Jan, 1998

Visiting Associate Professor, Department of Mathematics, Kiel University, Germany
1991 - Mar, 1993

Research Manager, C&C Information Technology Research Laboratories, NEC Corporation
Apr, 1981 - Mar, 1993

Research Laboratories, NEC Corporation
Sep, 1986 - May, 1988

Visiting Researcher, Wessex Institute of Technology, U.K.

Papers

GMRES using pseudoinverse for range symmetric singular systems

Kota Sugihara, Ken Hayami, Liao Zeyu

Journal of Computational and Applied Mathematics, 422 114865-114865, Apr, 2023 Peer-reviewed
GMRES Methods for Tomographic Reconstruction with an Unmatched Back Projector

Hansen, P.C, Hayami, K, Morikuni, K

Journal of Computational and Applied Mathematics (in press), 413 1-20, Oct, 2022 Peer-reviewed
A stabilized GMRES method for singular and severely ill-conditioned systems of linear equations

Liao, Z, Hayami, K, Morikuni, K, Yin, J.-F

Japan Journal of Industrial and Applied Mathematics, 39 717-751, Mar, 2022 Peer-reviewed
Kaczmarz-Type Inner-Iteration Preconditioned Flexible GMRES Methods for Consistent Linear Systems

Yi-Shu Du, Ken Hayami, Ning Zheng, Keiichi Morikuni, Jun-Feng Yin

SIAM Journal on Scientific Computing, S345-S366, Jun 14, 2021 Peer-reviewed
Corrigendum 2 to: A geometric view of Krylov subspace methods on singular systems

Hayami, K, Sugihara, K

Numerical Linear Algebra with Applications, 28 1-7, Feb, 2021 Peer-reviewedLead authorCorresponding author
Slime Mold Inspired Distribution Network Initial Solution

Verner Püvi, Robert J. Millar, Eero Saarijärvi, Tahitoa Arbelot, Ken Hayami, Matti Lehtonen

Energies, 13(23) 1-17, Nov 28, 2020 Peer-reviewed
Cluster Gauss-Newton method - An algorithm for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models

Aoki, Y, Hayami, K, Toshimoto, K, Sugiyama, Y

Optimization and Engineering (accepted for publication), 1-31, Oct, 2020 Peer-reviewed
Secant Variable Projection Method for Solving Separable Nonnegative Least Squares Problems

Song, X, Xu, W, Hayami, K, Zheng, N

Numerical Algorithms, 85 737-761, Mar 25, 2020 Peer-reviewed
Right Preconditioned MINRES for Singular Systems

Sugihara, K, Hayami, K, Zheng, N

Numerical Linear Algebra with Applications, 27(3) 1-25, Jan 24, 2020 Peer-reviewed
Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning

Cui, Y, ·Morikuni, K, Tsuchiya, T, Hayami, K

Computational Optimization and Applications (accepted), 74(1) 143-176, Jun, 2019 Peer-reviewed
The numerical solution of systems of nonlinear equations by an extension of the Hirano's method and Armijo's rule (in Japanese)

Ishii, M, Nunohiro, E, Hayami, K

Transactions of the Japan Society for Industrial and Applied Mathematics, 29(2) 225-249, Jun, 2019 Peer-reviewed
Modulus-based iterative methods for constrained Tikhonov regularization

Bai, Z.-Z, Buccini, A, Hayami, K, Reichel, L, Yin, J.-F, Zheng, N

Journal of Computational and Applied Mathematics, 319 1-13, Aug, 2017 Peer-reviewed
Updating preconditioners for modified least squares problems

Marin, J, Mas, J, Guerrero, D, Hayami, K

Numerical Algorithms, 75(2) 491-508, Jun, 2017 Peer-reviewed
Jacobian-Free Implicit Inner-Iteration Preconditioner for Nonlinear Least Squares Problems

Xu, W, Zheng, N, Hayami, K

Journal of Scientific Computing, 68(3) 1055-1081, Sep, 2016 Peer-reviewed
Right preconditioned MINRES using Eisenstat SSOR for positive semidefinite systems

Sugihara, K, Hayami, K, Zheng, N

Transactions of the Japan Society for Industrial and Applied Mathematics (in Japanese), 26(2) 124-166, Aug, 2016 Peer-reviewed
Modulus-type inner outer iteration methods for nonnegative constrained least squares problems

Ning Zheng, Ken Hayami, Jun-Feng Yin

SIAM Journal on Matrix Analysis and Applications, 37(3) 1250-1278, 2016 Peer-reviewed
Improvements to the cluster Newton method for underdetermined inverse problems

P. Gaudreau, K. Hayami, Y. Aoki, H. Safouhi, A. Konagaya

Journal of Computational and Applied Mathematics, 283 122-141, Aug, 2015 Peer-reviewed
Convergence of inner-iteration GMRES methods for rank-deficient least squares problems

Keiichi Morikuni, Ken Hayami

SIAM Journal on Matrix Analysis and Applications, 36(1) 225-250, 2015 Peer-reviewed
Cluster Newton method for sampling multiple solutions of underdetermined inverse problems : Application to a parameter identification problem in pharmacokinetics

Yasunori Aoki, Ken Hayami, Hans De Sterck, Akihiko Konagaya

SIAM Journal on Scientific Computing, 36(1) B14-B44, 2014 Peer-reviewed
FGMRES for linear discrete ill-posed problems

Morikuni, K., Reichel, L. and Hayami, K.

Applied Numerical Mathematics, 75 175-187, Jan, 2014 Peer-reviewedLast author

Books and Other Publications

ギルバート・ストラング著, 日本応用数理学会監訳, 今井桂子・岡本久監訳幹事, 世界標準MIT教科書ストラング：計算理工学

速水謙 (Role: Joint translator, 第7章大規模連立一次方程式一次方程式の解法, pp. 549-591)

近代科学社, Dec, 2016 (ISBN: 9784764904231)
応用数理ハンドブック (薩摩順吉, 大石進一, 杉原正顯編)

速水謙 (Role: Contributor, pp. 416-417, 最小二乗問題の数値解法)

朝倉書店, Oct, 2013
計算力学理論ハンドブック (萩原一郎, 田端正久監訳)

速水謙, 大西和榮 (Role: Contributor, pp. 355-393, 13章境界要素法と有限要素法の結合)

朝倉書店, Jun, 2010 (ISBN: 9784254231205)
岩波数学辞典第4版 (日本数学会編集)

速水謙, 室田一雄 (Role: Contributor, pp. 387-392, 固有値の数値計算法)

岩波書店, Mar, 2007 (ISBN: 4000802097)
A Projection Transformation Method for Nearly Singular Surface Boundary Element Integrals (Lecture Notes in Engineering, Vol. 73)

Hayami, K

Springer Verlag, 456 pages, Jan, 1992 (ISBN: 3540550003)

Major Presentations

240

On breakdown of GMRES for non-range-symmetric systems

Hayami, K, Sugihara, K

The 20th Joint Meeting of Special Activity Groups, The Japan Society of Industrial and Applied Mathematics, Mar 5, 2024, The Japan Society of Industrial and Applied Mathematics

Teaching Experience

Misc.

149

NR-SSOR right preconditioned RRGMRES for arbitrary singular systems and least squares problems

arXiv, 2504.09891 1-36, Apr, 2025 Last author
Convergence analysis of inner-iteration preconditioned GMRES

Liao, Z, Hayami, K

arXiv、Mathematics > Numerical Analysi、, 1-15, Aug 2, 2024
Report on the RIMS Symposium (Open): Research on High-Performance Scientific Computing in a New Era

Ken Hayami

Bulletin of the Japan Society for Industrial and Applied Mathematics (JSIAM), 34(2) 71-72, Jun, 2024 InvitedLead author
Right preconditioned GMRES for arbitrary singular systems

Kota Sugihara, Ken Hayami

arXiv、Mathematics, Numerical Analysis, 1-25, Oct 25, 2023 Corresponding author
47

言葉としての数理

速水謙

応用数理, 33(3) 1-1, Sep 25, 2023 InvitedLead author
GMRES using pseudo-inverse for range symmetric singular systems

Sugihara, K, Hayami, K, Liao, Z

arXiv, Mathematics, Numerical Analysis, 1-15, Jan 28, 2022
GMRES Methods for Tomographic Reconstruction with an Unmatched Back Projector

Hansen, P.C, Hayami, K, Morikuni, K

arXiv, Mathematics, Numerical Analysis, 1-25, Oct 4, 2021
GMRES on singular systems revisited

Hayami, K, Sugihara, K

arXiv, Mathematics, Numerical Analysis, 1-13, Sep 2, 2020 Lead author
Kaczmarz-type inner-iteration preconditioned flexible GMRES methods for consistent linear systems

Yi-Shu Du, Ken Hayami, Ning Zheng, Keiichi Morikuni, Jun-Feng Yin

NII Technical Reports, arXiv, Jun 18, 2020
A Stabilized GMRES Method for Solving Underdetermined Least Squares Problems

Zeyu LIAO, Ken HAYAMI, Keiichi MORIKUNI, and Jun-Feng YIN

NII Technical Reports, arXiv, NII-2020(001E) 1-20, Mar, 2020
Convergence of the Conjugate Gradient Method on Singular Systems

Ken Hayami

NII Technical Reports, arXiv, NII-2018(001E) 1-7, Sep 4, 2018
Cluster Gauss-Newton method for finding multiple approximate minimisers of nonlinear least squares problems with applications to parameter estimation of pharmacokinetic models

Yasunori Aoki, Ken Hayami, Kota Toshimoto, Yuichi Sugiyama

NII Technical Report, NII-2020(002E) 1-32, Aug 20, 2018
数理の楽しみ

速水謙

応用数理, 28(3) 3-3, 2018 InvitedLead author
Implementation of Interior-Point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning

Cui, Y, Morikuni, K, Tsuchiya, T, Hayami, K

NII Technical Reports, National Institute of Informatics, Tokyo, arXiv, NII-2016(003E) 1-27, May, 2016
第8回国際応用数理会議ICIAM2015(北京)に参加して

Ken Hayami

JSIAM Online Magazine, Nov, 2015 Invited
Modulus-Type Inner Outer Iterative Methods for Nonnegative Constrained Least Squares Problems

Zheng, N, Hayami, K, Yin, J.-F

NII Technical Reports, National Institute of Informatics, Tokyo, NII-2015(001E) 1-23, Jan, 2015
Cluster Newton method for underdetermined inverse problems and its application to pharmacokinetic models

Aoki, Y, Hayami, K, Konagaya, A

Bulletin of the Japan Society for Industrial and Applied Mathematics, 24(4) 7-15, Dec, 2014 Peer-reviewedInvited
Modulus inner-outer iterative method for nonnegative constrained least squares problems

Zheng, N, Hayami, K, Yin, J.-F

2014 Annual Meeting of the Japan Society for Industrial and Applied Mathematics, National Graduate Institute for Policy Studies, Tokyo, Sep 3, 2014
Jacobian-Free Three-Level Trust Region Method for Nonlinear Least Squares Problems

Xu, W, Zheng, N, Hayami, K

NII Technical Reports, National Institute of Informatics, Tokyo, NII-2014(003E) 1-22, Sep, 2014
Convergence of inner-iteration GMRES methods for least squares problems (Revised)

Morikuni, K, Hayami, K

NII Technical Reports, National Institute of Informatics, Tokyo, NII-2013-004E 1-24, Dec, 2013

Professional Memberships

- Present

Society for Industrial and Applied Mathematics (SIAM)
- Present

日本応用数理学会
- Present

The Chem-Bio Informatics Society
- Mar, 2021

情報処理学会
- Mar, 2021

日本計算工学会
- Mar, 2021

日本シミュレーション学会
- Mar, 2021

日本数学会

Awards

Research Projects

The development of a virtual clinical experiment system considering the variation of governing causes of the transportation of drugs among organisms, drug effect, and side effects.

Grants-in-Aid for Scientific Research (B) (KAKENHI), Japan Society for the Promotion of Science, Apr, 2019 - Mar, 2022

Yuuichi Sugiyama
The Deepening and New Developments in Mathematical Modelling of Linear Programming on Convex Cones

Grants-in-Aid for Scientific Research (B), MInistry of Education, Culture, Sports, Science and Technology in Japan, Apr, 2015 - Mar, 2018

Takashi Tsuchiya
Fast Solution Methods for Least Squares Problems and their Applications

Grants-in-Aid for Scientific Research (C), MInistry of Education, Culture, Sports, Science and Technology in Japan, Apr, 2015 - Mar, 2018

Ken Hayami
Design and Implementation of Chemical Reaction Circuits for Molecular Robots with Intelligence

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area), Japan Society for the Promotion of Science, Jun, 2012 - Mar, 2017

Kobayashi Satoshi, Yokomori Takashi, Imura Junichi, Hayami Ken, Yannick Rondelez
The Iterative Solution of Least Squares Problems and its Application to Inverse Problems

Grants-in-Aid for Scientific Research (C), MInistry of Education, Culture, Sports, Science and Technology in Japan, Apr, 2012 - Mar, 2014

Ken Hayami
The Solution of Least Squares Problems Using Krylov Subspace Methods

Grants-in-Aid for Scientific Research(基盤研究(C)), 基盤研究(C), Ministry of Education, Culture, Sports, Science and Technology, 2009 - 2011

Ken HAYAMI
Mathematical problems and the comprehensive development of fast solvers for ultra large systems of linear equations occurring in scientific computing.

KAKENHI (B), Japan Society for the Promotion of Science, Apr, 2003 - Mar, 2007

Shiao-Liang Zhang
Research on Krylov Subspace Type Iterative Solvers for Large Scale Systems of Equations and Least Squares Problems

Grants-in-Aid for Scientific Research(基盤研究(C)), 基盤研究(C), Ministry of Education, Culture, Sports, Science and Technology, 2005 - 2007

Ken HAYAMI
Fast Implementation of the Boundary Element Method and its Application to Inverse Problems

Grants-in-Aid for Scientific Research(基盤研究(C)), 基盤研究(C), Ministry of Education, Culture, Sports, Science and Technology, 2000 - 2002

Ken HAYAMI, Tetsushi NISHIDA, Takaaki NARA
Robust Implementation of 4-D Geometric Algorithm and Applications

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Japan Society for the Promotion of Science, 1998 - 2000

SUGIHARA Kokichi, INAGAKI Hiroshi, NISHIDA Tetsushi, HAYAMI Ken, IMAI Toshiyuki
Design of Precision-Guaranteed Geometric Algorithms

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research on Priority Areas (B), Japan Society for the Promotion of Science, 1998 - 2000

SUGIHARA Kokichi, IMAI Toshiyuki, YAMAMOTO Osami, HAYAMI Ken, HIYOSHI Hisamoto, NISHIDA Tetsushi
境界要素法の高速化とその応用

研究助成, 大川情報通信基金, Apr, 1997 - Mar, 1998

速水謙
乱れた格子の上でも動作する有限要素法の開発

科学研究費助成事業, 萌芽的研究, 日本学術振興会, 1997 - 1998

杉原厚吉, 今井敏行, 速水謙
Image Processing Based on Spline Representation

Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science, 1995 - 1996

SUGIHARA Kokichi, IMAI Toshiyuki, HAYAMI Ken, OKABE Yasunori
The Research on Making the Boundary Element Method Highly Accurate and Efficient

Grants-in-Aid for Scientific Research(一般研究(C), 基盤研究(C)), 一般研究(C), 基盤研究(C), Ministry of Education, Culture, Sports, Science and Technology, 1994 - 1996

Ken HAYAMI, Toshiyuki IMAI
Construction of a Topology-Oriented Geometric System

Grants-in-Aid for Scientific Research, Grant-in-Aid for Developmental Scientific Research (B), Japan Society for the Promotion of Science, 1993 - 1995

SUGIHARA Kokichi, IMAI Toshiyuki, HAYAMI Ken
Design of numerically robust geometric algorithms

Grants-in-Aid for Scientific Research, Grant-in-Aid for General Scientific Research (B), Japan Society for the Promotion of Science, 1992 - 1994

SUGIHARA Kokichi, IMAI Toshiyuki, HAYAMI Ken