Kensuke Aishima
Research fields　[Japanese]
Numerical linear algebra
Update:2023/5/30
Refereed papers
  • K. Aishima: Strong consistency of the projected total least squares dynamic mode decomposition for datasets with random noise, Jpn. J. Ind. Appl. Math., vol. 40 (2023), pp. 691--707, https://doi.org/10.1007/s13160-022-00547-6
  • K. Aishima: Statistical modeling and an adaptive averaging technique for strong convergence of the dynamic mode decomposition, J. Comput. Appl. Math. 417 (2023), Paper No. 114551, https://doi.org/10.1016/j.cam.2022.114551
  • K. Aishima: Consistent estimation for an errors-in-variables model based on constrained total least squares problems, JSIAM Lett. 14 (2022), 111-114
  • K. Aishima: Formulations and theorems of quadratically convergent methods for inverse symmetric eigenvalue problems, Nonlinear Theory and Its Applications, IEICE, vol. 11 (2020), pp. 303--326
  • K. Aishima: Strong convergence for the dynamic mode decomposition based on the total least squares to noisy datasets, JSIAM Letters, vol. 12 (2020), pp. 33--36
  • K. Aishima: Convergence proof of the Harmonic Ritz pairs of iterative projection methods with restart strategies for symmetric eigenvalue problems, Jpn. J. Ind. Appl. Math., vol. 37 (2020), pp. 415--431, https://doi.org/10.1007/s13160-019-00402-1
  • T. Ogita, K. Aishima: Iterative refinement for singular value decomposition based on matrix multiplication, Journal of Computational and Applied Mathematics, vol. 369 (2020), 112512.
  • K. Aishima: A quadratically convergent algorithm for inverse generalized eigenvalue problems, Journal of Computational and Applied Mathematics, vol. 367 (2020), 112485.
  • T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition II: clustered eigenvalues, Jpn. J. Ind. Appl. Math., vol. 36 (2019), pp. 435--459
  • T. Ogita, K. Aishima: Iterative refinement for symmetric eigenvalue decomposition, Jpn. J. Ind. Appl. Math., vol. 35 (2018), pp. 1007--1035
  • K. Aishima: A quadratically convergent algorithm for inverse eigenvalue problems with multiple eigenvalues, Linear Algebra and its Applications, vol. 549 (2018), pp. 30--52.
  • Y. Morijiri, K. Aishima and T. Matsuo: Extension of an error analysis of the randomized Kaczmarz method for inconsistent linear systems, JSIAM Letters, vol. 10 (2018), pp. 17--20
  • K. Aishima: A quadratically convergent algorithm based on matrix equations for inverse eigenvalue problems, Linear Algebra and its Applications, vol. 542 (2018), pp. 310--333.
  • K. Aishima: On convergence of iterative projection methods for symmetric eigenvalue problems, Journal of Computational and Applied Mathematics, vol. 311 (2017), 513--521.
  • K. Aishima: A note on the convergence theorem of the tridiagonal QR algorithm with Wilkinson's shift, Japan Journal of Industrial and Applied Mathematics, vol. 32 (2015), pp. 465--487.
  • T. Tsuchiya, K. Aishima: A note on convergence and a posteriori error estimates of the classical Jacobi method, Nonlinear Theory and Its Applications, IEICE, vol. 6 (2015), pp. 391--396.
  • K. Aishima: Global Convergence of the Restarted Lanczos and Jacobi-Davidson Methods for Symmetric Eigenvalue Problems, Numerische Mathematik, vol. 131 (2015), pp. 405-423.
  • S. Ito, K. Aishima, T. Nara, M. Sugihara: Orthogonal Polynomial Approach to Estimation of Poles of Rational Functions from Data on Open Curves, Journal of Computational and Applied Mathematics, vol. 273 (2015), pp. 326-345.
  • K. Aishima: A Note on the Rayleigh Quotient Iteration for Symmetric Eigenvalue Problems, Japan Journal of Industrial and Applied Mathematics, vol. 31 (2014), pp. 575--581.
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: A shift strategy for superquadratic convergence in the dqds algorithm for singular values, Journal of Computational and Applied Mathematics, vol. 257 (2014), 132--143.
  • Y. Nakatsukasa, K. Aishima, I. Yamazaki: dqds with Aggressive Early Deflation, SIAM Journal on Matrix Analysis and Applications, vol. 33 (2012), pp. 22--51.
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: A Wilkinson-like Multishift QR Algorithm for Symmetric Eigenvalue Problems and Its Global Convergence, Journal of Computational and Applied Mathematics, vol. 236 (2012), 3556--3560.
  • K. Aishima, T. Matsuo, K. Murota: A Note on the dqds Algorithm with Rutishauser's Shift for Singular Values, Japan Journal of Industrial and Applied Mathematics, vol. 28 (2011), pp. 251--262.
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: A Survey on Convergence Theorems of the dqds Algorithm for Computing Singular Values, Journal of Math-for-Industry, vol. 2 (2010), pp. 1--11.
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: Superquadratic Convergence of DLASQ for Computing Matrix Singular Values, Journal of Computational and Applied Mathematics, vol. 234 (2010), 1179--1187.
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: Superquadratically Convergent Shift Strategy with Theoretical Guarantee in the dqds Algorithm for Singular Values, Transactions of the Japan Society for Industrial and Applied Mathematics, vol. 18 (2008), pp. 285--302. (in Japanese)
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: On Convergence of the dqds Algorithm for Singular Value Computation, SIAM Journal on Matrix Analysis and Applications, vol. 30 (2008), pp. 522--537.
    [EASIAM Student Paper Prize (2010)]
  • K. Aishima, T. Matsuo, K. Murota: Rigorous Proof of Cubic Convergence for the dqds Algorithm for Singular Values, Japan Journal of Industrial and Applied Mathematics, vol. 25 (2008), pp. 65--81.
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: On Convergence of dqds and mdLVs Algorithms for Singular Value Computation, Transactions of the Japan Society for Industrial and Applied Mathematics, vol. 17 (2007), pp. 97--131. (in Japanese)
    [JSIAM Best paper award (2008)]
    Talks
  • K. Aishima: On convergence of the dynamic mode decomposition for noisy datasets, 2021 Second Workshop on Numerical Algebra, Algorithms and Analysis (SWNAAA2021), online
  • K. Aishima: Newton-like methods for inverse eigenvalue problems, 2019 Mini-Workshop on Computational Science (MWCS2019), Dalian
  • K. Aishima: Convergence theorem of iterative projection methods for symmetric eigenvalue problems, 9th International Congress on Industrial and Applied Mathematics (ICIAM2019), Valencia.
  • K. Aishima: A quadratically convergent algorithm for inverse generalized eigenvalue problems, The 18th International Symposium on Scientific Computing, Computer Arithmetic, and Verified Numerical Computations (SCAN2018), Tokyo
  • K. Aishima: Matrix Multiplication Based Algorithm for Inverse Eigenvalue Problems and Its Quadratic Convergence, 18th SIAM Conference on Parallel Processing for Scientific Computing, 2018, Tokyo
  • K. Aishima: A Quadratically Convergent Algorithm Based on Matrix Equations for Inverse Eigenvalue Problems, The Householder Symposium XX, Spa, 2017, The Inn at Virginia Tech
  • T. Ogita and K. Aishima: Iterative Refinement for Eigenvectors of Symmetric Matrices with Clustered Eigenvalues, 2017 SIAM Conference on Computational Science and Engineering, Atlanta.
  • K. Aishima: A quadratically convergent method for inverse eigenvalue problems, Sapporo Summer HPC Seminar 2016.
  • K. Aishima: A quasi-Newton method for inverse eigenvalue problems, 20th Conference of the International Linear Algebra Society, Leuven, 2016.
  • K. Aishima, T. Ogita: Iterative Refinement for Symmetric Eigenvalue Decomposition and Singular Value Decomposition, SIAM Conference on Applied Linear Algebra, Atlanta, 2015.
  • K. Aishima: Convergence Proof for Some Iterative Projection Methods from a Perturbation Bound for Symmetric Eigenvalue Problems, 8th International Congress on Industrial and Applied Mathematics (ICIAM2015), Beijing (Aug. 10--14, 2015).
  • K. Aishima: Global Convergence of the Restarted Lanczos Method and Jacobi-Davidson Method for Symmetric Eigenvalue Problems, The Householder Symposium XIX, Spa, 2014
  • K. Aishima: Global Convergence of the Restarted Lanczos Method, International Workshop on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014), Tsukuba, 2014
  • K. Aishima: A Wilkinson-like Multishift QR Algorithm for Symmetric Eigenvalue Problem and Its Global Convergence, NLA group meeting, Manchester, 2012.
  • K. Aishima, Takayasu Matsuo, Masaaki Sugihara: A note on the Rayleigh quotient iteration for symmetric eigenvalue problems, International Congress on Computational and Applied Mathematics (ICCAM2012), Ghent, 2012.
  • K. Aishima, Yuji Nakatsukasa, Ichitaro Yamazaki: dqds with aggressive early deflation for computing singular values, SIAM Conference on Applied Linear Algebra, Valencia, 2012.
  • K. Aishima, Yuji Nakatsukasa, Ichitaro Yamazaki: Stability theorem of the dqds with aggressive deflation for singular values, 9th International Workshop on Accurate Solution of Eigenvalue Problems, California, 2012.
  • K. Aishima, Yuji Nakatsukasa, Ichitaro Yamazaki: dqds with aggressive deflation for singular values, 12th Advanced Supercomputing Environment (ASE) Seminar, Tokyo, 2012.
  • K. Aishima: A shift strategy for superquadratic convergence of the dqds algorithm for computing singular values, An NWO-JSPS Joint Seminar, Delft, 2012.
  • K. Aishima: Dqds Algorithm with Aggressive Deflation for Computing Singular Values, LAPACK Seminar, California, 2012
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: Complete Analysis of Convergence Rate of the Tridiagonal QR Algorithm with Wilkinson's Shift, 7th International Congress on Industrial and Applied Mathematics (ICIAM2011), Vancouver (Jul. 18--22, 2011).
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: Global Convergence of Wilkinson-like Multishift QR Algorithmfor Symmetric Eigenvalue Problems, International Congress on Computational and Applied Mathematics (ICCAM2010), Leuven (Jul. 5--9, 2010).
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: On Convergence of the dqds Algorithm for Singular Value Computation, The 6th East Asia SIAM Conference, Kuala Lumpur (Jun. 22--24, 2010). [1st Prize of EASIAM Student Paper Competition (2010)]
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: A Note on the dqds Algorithm with Rutishauser's Shift, SIAM Conference on Applied Linear Algebra, California (Oct. 26--29, 2009).
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: A Shift Strategy for Superquadratic Convergence in the dqds Algorithm for Singular. Values, The 14th International Congress on Computational and Applied Mathematics (ICCAM2009), Antalya (Sep. 29--Oct. 2, 2009).
  • K. Aishima, T. Matsuo, K. Murota, M. Sugihara: Superquadratic Convergence of DLASQ for Computing Matrix Singular Values, The 13th International Congress on Computational and Applied Mathematics (ICCAM2008), Ghent (Jul. 7--11, 2008).
    Awards
  • 1st Prize of EASIAM Student Paper Competition (2010)
  • Best paper award in Japan Society for Industrial and Applied Mathematics, 2008.
  • Best presentation award in Japan Society for Industrial and Applied Mathematics, 2006.
    METR
  • Kensuke Aishima: A Quadratically Convergent Algorithm for Inverse Eigenvalue Problems with Multiple Eigenvalues, METR 2017-17, Department of Mathematical Informatics, University of Tokyo (2017).
  • Kensuke Aishima: A Quadratically Convergent Algorithm Based on Matrix Equations for Inverse Eigenvalue Problems, METR 2016-16, Department of Mathematical Informatics, University of Tokyo (2016).
  • Takeshi Ogita, Kensuke Aishima: Iterative Refinement for Symmetric Eigenvalue Decomposition Adaptively Using Higher-Precision Arithmetic, METR 2016-11, Department of Mathematical Informatics, University of Tokyo (2016).
  • Kensuke Aishima: On Convergence of Iterative Projection Methods for Symmetric Eigenvalue Problems, METR 2015-25, Department of Mathematical Informatics, University of Tokyo (2015).
  • Kensuke Aishima: Global Convergence of the Restarted Lanczos Method and Jacobi-Davidson Method for Symmetric Eigenvalue Problems, METR 2013-27, Department of Mathematical Informatics, University of Tokyo (2013).
  • Kensuke Aishima, Takayasu Masaaki Sugihara: A Complete Analysis of Convergence Rate of the Tridiagonal QR Algorithm with Wilkinson’s Shift, METR 2013-26, Department of Mathematical Informatics, University of Tokyo (2013).
  • Kensuke Aishima, Takayasu Matsuo, Kazuo Murota, Masaaki Sugihara: A Survey on Convergence Theorems of the dqds Algorithm for Computing Singular Values, METR 2009-52, Department of Mathematical Informatics, University of Tokyo (2009).
  • Kensuke Aishima, Takayasu Matsuo, Kazuo Murota: Rigorous Proof of Cubic Convergence for the dqds Algorithm for Singular Values, METR 2007-15, Department of Mathematical Informatics, University of Tokyo (2007).
  • Kensuke Aishima, Takayasu Matsuo, Kazuo Murota, Masaaki Sugihara: A Shift Strategy for Superquadratic Convergence in the dqds Algorithm for Singular Values, METR 2007-12, Department of Mathematical Informatics, University of Tokyo (2007).
  • Kensuke Aishima, Takayasu Matsuo, Kazuo Murota, Masaaki Sugihara: On Convergence of the dqds Algorithm for Singular Value Computation, METR 2006-59, Department of Mathematical Informatics, University of Tokyo (2006).
    Proceedings
  • K. Aishima, T. Matsuo, K. Murota, and M. Sugihara: Convergence theorems of the dqds algorithm for singular values, RIMS Kokyuroku 1614 (2008) 20--33 (in Japanese).
  • K. Aishima, T. Matsuo, K. Murota, and M. Sugihara: On Convergence of the dqds and mdLVs Algorithms for Computing Matrix Singular Values, RIMS Kokyuroku 1573 (2007) 106--117
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