Michiel Hochstenbach

Publications Michiel Hochstenbach

Accepted | Journal papers | Preprints | PhD Thesis | Proceedings | Various

Acknowledgment: This research has been partially supported by

Profile on Google Scholar | Publications on Google Scholar

Latest preprints

Journal papers

(reverse chronological order)
  1. P.Y. Gidisu, M.E. Hochstenbach
    A restricted SVD type CUR decomposition for matrix triplets
    SIAM J. Sci. Comp. (preprint)

  2. M.E. Hochstenbach, T. Kosir, B. Plestenjak
    On the solution of rectangular multiparameter eigenvalue problems
    Num. Lin. Alg. Appl. 31(2), 2024 (preprint)

  3. L. Xia, S. Massei, M.E. Hochstenbach, B. Koren
    On stochastic roundoff errors in gradient descent with low-precision floating-point computation
    J. Opt. Theory Appl. 2023 (preprint)

  4. M.E. Hochstenbach, C. Mehl, B. Plestenjak
    Solving singular generalized eigenvalue problems. Part II: projection and augmentation
    SIAM J. Matrix Anal. Appl. 44(4), 2023 (preprint)

  5. G. Ferrandi, M.E. Hochstenbach
    A homogeneous Rayleigh quotient with applications in gradient methods
    J. Comput. Appl. Math. 437, pp 75–106, 2023 (preprint)

  6. G. Ferrandi, M.E. Hochstenbach, N. Krejic
    A harmonic framework for stepsize selection in gradient methods
    Comput. Optim. Appl. 85, pp 75–106, 2023 (preprint)

  7. P.Y. Gidisu, M.E. Hochstenbach
    A hybrid DEIM and leverage scores based method for CUR index selection
    In: Progress in Industrial Mathematics at ECMI 2021, pp 147-153, 2022 (preprint)

  8. P.Y. Gidisu, M.E. Hochstenbach
    A generalized CUR decomposition for matrix pairs
    SIAM J. Math. Data Science 4(1), 386-409, 2022 (preprint)
    Perfect Gidisu has won a 2023 SIAM Student Prize for this paper

  9. G. Pio, S.C. Hess, M.E. Hochstenbach, M. Ceci
    BROCCOLI - overlapping and outlier-robust biclustering through proximal stochastic gradient descent
    Data Mining and Knowledge Discovery, 2021

  10. B.S. van Lith, P.C. Hansen, M.E. Hochstenbach
    A twin error gauge for Kaczmarz's iterations
    SIAM J. Sci. Comp., S173-S199, 2021 (preprint)

  11. M.E. Hochstenbach, B. Plestenjak
    Computing several eigenvalues of nonlinear eigenvalue problems by selection
    Calcolo 57(2), 2020 (preprint)

  12. M.E. Hochstenbach, C. Mehl, B. Plestenjak
    Solving singular generalized eigenvalue problems by a rank-completing perturbation
    SIAM J. Matrix Anal. Appl. 40(3), 1022-1046, 2019 (pdf)

  13. M.E. Hochstenbach, K. Meerbergen, E. Mengi, B. Plestenjak
    Subspace methods for 3-parameter eigenvalue problems
    Num. Lin. Alg. Appl. 26, 2019 (preprint)

  14. Y. Dong, P.C. Hansen, M.E. Hochstenbach, N.A.B. Riis
    Fixing nonconvergence of algebraic iterative reconstruction with an unmatched backprojector
    SIAM J. Sci. Comp. 41(3), A1822-A1839, 2019 (pdf)

  15. A. Boralevi, J. Draisma, J. van Doornmalen, M.E. Hochstenbach, B. Plestenjak
    Uniform determinantal representations
    SIAM J. Alg. Geom. Appl. 1(1), 415-441, 2017 (pdf)

  16. I.N. Zwaan, M.E. Hochstenbach
    Krylov-Schur type restarts for the two-sided Arnoldi method
    SIAM J. Matrix Anal. Appl. 38(2), 297-321, 2017 (pdf)

  17. I.N. Zwaan, M.E. Hochstenbach
    Multidirectional subspace expansion for one-parameter and multiparameter Tikhonov regularization
    J. Sci. Comp. 70(3), 990-1009, 2017

  18. A. Koskela, E. Jarlebring, M.E. Hochstenbach
    Krylov approximation of linear ODEs with polynomial parameterization
    SIAM J. Matrix Anal. Appl. 37(2), 518-538, 2016 (pdf)

  19. B. Plestenjak, M.E. Hochstenbach
    Roots of bivariate polynomial systems via determinantal representations
    SIAM J. Sci. Comp. 38(2), A765-A788, 2016 (pdf)

  20. S.W. Gaaf, M.E. Hochstenbach
    Probabilistic bounds for the matrix condition number with extended Lanczos bidiagonalization
    SIAM J. Sci. Comp. 37(5), S581-S601, 2015 (pdf)

  21. M.E. Hochstenbach, L. Reichel, X. Yu
    A Golub-Kahan-type reduction method for matrix pairs
    J. Sci. Comp. 65(2), 767-789, 2015 (preprint)

  22. M.E. Hochstenbach, S. Noschese, L. Reichel
    Fractional regularization matrices for linear discrete ill-posed problems
    J. Engin. Math. 93(1), 113-129, 2015 (preprint)

  23. B. Plestenjak, C.I. Gheorghiu, M.E. Hochstenbach
    Spectral collocation for multiparameter eigenvalue problems arising from separable boundary value problems
    J. Comp. Phys. 298, 585-601, 2015 (preprint)

  24. M.E. Hochstenbach, A. Muhic, B. Plestenjak
    Jacobi-Davidson methods for polynomial two-parameter eigenvalue problems
    J. Comp. Appl. Math. 288, 251-263, 2015 (preprint)

  25. M.E. Hochstenbach, L. Reichel, G. Rodriguez
    Regularization parameter determination for discrete ill-posed problems
    J. Comp. Appl. Math. 273, 132-149, 2015 (preprint)

  26. M.E. Hochstenbach
    Probabilistic upper bounds for the matrix two-norm
    J. Sci. Comp. 57 (3), 464-476, 2013 (preprint)

  27. I.W.M. Bleylevens, M.E. Hochstenbach, R.L.M. Peeters
    Polynomial optimization and a Jacobi-Davidson type method for commuting matrices
    Appl. Math. Comput. 224, 564-580, 2013 (preprint)

  28. M.E. Hochstenbach, D.A. Singer, P.F. Zachlin
    Numerical approximation of the field of values of the inverse of a large matrix
    Textos de Matematica 429, special issue in honor of Prof. Bebiano, 2013 (preprint)

  29. B. Besselink, A. Lutowska, U. Tabak, N. van de Wouw, H. Nijmeijer, M.E. Hochstenbach, W.H.A. Schilders, D.J. Rixen
    A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control
    J. Sound Vibrat. 332 (19), 4403-4422, 2013 (preprint)

  30. P.-A. Absil, M.E. Hochstenbach
    A differential-geometric look at the Jacobi-Davidson framework
    Invited book chapter in: K. Hüper and J. Trumpf (eds.), On State Observers
    Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday,
    CreateSpace, 2013, ISBN 978-1470044008. (preprint) (see also here)

  31. C.I. Gheorghiu, M.E. Hochstenbach, B. Plestenjak, J. Rommes
    Spectral collocation solutions to multiparameter Mathieu's system
    Appl. Math. Comput. 218 (24), 11990-12000, 2012. (preprint)

  32. M.E. Hochstenbach, N. McNinch, L. Reichel
    Discrete ill-posed least-squares problems with a solution norm constraint
    Lin. Alg. Appl. 436 (10), 3801-3818, 2012 (preprint)

  33. M.E. Hochstenbach, A. Muhic, B. Plestenjak
    On linearizations of the quadratic two-parameter eigenvalue problems
    Lin. Alg. Appl. 436 (8), 2725-2743, 2012 (preprint)

  34. M.E. Hochstenbach, L. Reichel
    Combining approximate solutions for linear discrete ill-posed problems
    J. Comp. Appl. Math. 236 (8), 2179-2185, 2012. (preprint)

  35. M.E. Hochstenbach, L. Reichel
    Fractional Tikhonov regularization for linear discrete ill-posed problems
    BIT 51 (1), 197-215, 2011

  36. M.E. Hochstenbach
    Fields of values and inclusion regions for matrix pencils
    Electr. Trans. Num. Anal. 38, 98-112, 2011. (bibtex)

  37. M.E. Hochstenbach, L. Reichel
    Subspace-restricted singular value decompositions for linear discrete ill-posed problems
    J. Comp. Appl. Math. 235 (4), 1053-1064, 2010. (preprint)

  38. M.E. Hochstenbach, L. Reichel
    An iterative method for Tikhonov regularization with a general linear regularization operator
    J. Integral Equations Appl. 22, 463-480, 2010 (preprint, bibtex)

  39. M.E. Hochstenbach
    A Jacobi-Davidson type method for the generalized singular value problem
    Lin. Alg. Appl. 431, 471-487, 2009 (preprint, bibtex)

  40. E. Jarlebring, M.E. Hochstenbach
    Polynomial two-parameter eigenvalue problems and matrix pencil methods
    for stability of delay-differential equations
    Lin. Alg. Appl. 431, 369-380, 2009 (preprint, bibtex)

  41. M.E. Hochstenbach, Y. Notay
    Controlling inner iterations in the Jacobi-Davidson method
    SIAM. J. Matrix Anal. Appl. 31 (2), 460-477, 2009 (© SIAM 2009, preprint, bibtex)

  42. M.E. Hochstenbach, D.A. Singer, P.F. Zachlin
    Eigenvalue inclusion regions from inverses of shifted matrices
    Lin. Alg. Appl. 429, 2481-2496, 2008 (preprint, bibtex)

  43. M.E. Hochstenbach, B. Plestenjak
    Harmonic Rayleigh-Ritz extraction for the multiparameter eigenvalue problem
    Electr. Trans. Num. Anal. 29, 81-96, 2008. (bibtex)

  44. M.E. Hochstenbach, G.L.G. Sleijpen
    Harmonic and refined Rayleigh-Ritz for the polynomial eigenvalue problem
    Num. Lin. Alg. Appl. 15 (1), 35-54, 2008. (preprint, bibtex)

  45. P.F. Zachlin, M.E. Hochstenbach
    On the numerical range of a matrix
    Linear and Multilinear Algebra 56 (1-2), 185-225, 2008. (preprint, bibtex)
    English translation with comments and corrections of
    R. Kippenhahn, Über den Wertevorrat einer Matrix, Mathematische Nachrichten, 6 (3-4), 193-228, 1951.

  46. M.E. Hochstenbach
    A Jacobi-Davidson type method for the product eigenvalue problem
    J. Comp. Appl. Math. 212 (1), 46-62, 2008. (preprint, bibtex)

  47. M.E. Hochstenbach, Y. Notay
    Homogeneous Jacobi-Davidson
    Electr. Trans. Num. Anal. 29, 19-30, 2007. (bibtex)

  48. M.E. Hochstenbach, Y. Notay
    The Jacobi-Davidson method
    GAMM Mitteilungen 29 (2), 368-382, 2006. (bibtex)
    Invited paper, Themenheft Applied and Numerical Linear Algebra, Part II.

  49. M.E. Hochstenbach
    Generalizations of harmonic and refined Rayleigh-Ritz
    Electr. Trans. Num. Anal. 20, 235-252, 2005. (bibtex)

  50. M.E. Hochstenbach, T. Kosir, B. Plestenjak
    A Jacobi-Davidson type method for the two-parameter eigenvalue problem
    SIAM J. Matrix Anal. Appl. 26 (2), 477-497, 2005 (pdf, bibtex)

  51. M.E. Hochstenbach
    Harmonic and refined extraction methods for the singular value problem,
    with applications in least squares problems
    BIT 44 (4), 721-754, 2004. (preprint, bibtex)
    Winner 2003 SIAM student paper competition at 2003 SIAM annual meeting
    Winner of student/new PhD paper competition award at IMACS Conference 2003

  52. P. Arbenz, M.E. Hochstenbach
    A Jacobi-Davidson method for solving complex symmetric eigenvalue problems
    SIAM J. on Sci. Comp. 25 (5), 1655-1673, 2004 (pdf, bibtex)

  53. M.E. Hochstenbach, B. Plestenjak
    Backward error, condition numbers, and pseudospectrum for the multiparameter eigenvalue problem
    Lin. Alg. Appl. 375, 63-81, 2003 (preprint, bibtex)

  54. M.E. Hochstenbach, H.A. van der Vorst
    Alternatives to the Rayleigh quotient for the quadratic eigenvalue problem
    SIAM J. on Sci. Comp. 25 (2), 591-603, 2003 (pdf, bibtex)
    Winner of student/new PhD paper competition award at Copper Mountain Conference 2002

  55. M.E. Hochstenbach, G.L.G. Sleijpen
    Two-sided and alternating Jacobi-Davidson
    Lin. Alg. Appl. 358 (1-3), 145-172, 2003 (preprint, bibtex)

  56. M.E. Hochstenbach, B. Plestenjak
    A Jacobi-Davidson type method for a right definite two-parameter eigenvalue problem
    SIAM J. on Matrix Anal. Appl. 24 (2), 392-410, 2002 (© SIAM 2002, pdf, bibtex)
    Winner of poster competition at IWASEP4, 2002

  57. M.E. Hochstenbach
    A Jacobi-Davidson type SVD method
    SIAM J. on Sci. Comp. 23 (2), 606-628, 2001 (pdf, bibtex)
    Second place student paper competition at Copper Mountain Conference 2000

  58. J.L.M. van Dorsselaer, M.E. Hochstenbach, H.A. van der Vorst
    Computing probabilistic bounds for extreme eigenvalues
    of symmetric matrices with the Lanczos method
    SIAM J. on Matrix Anal. Appl. 22 (3), 837-852, 2000 (pdf, bibtex)

Technical reports / preprints

(chronological order)
  1. M. Hochbruck, M.E. Hochstenbach
    Subspace extraction for matrix functions
  2. M.E. Hochstenbach
    Variations on harmonic Rayleigh-Ritz for standard and generalized eigenproblems
  3. W. Dijkstra, M.E. Hochstenbach
    Numerical approximation of the logarithmic capacity

Ph.D. Thesis

Subspace Methods for Eigenvalue Problems
M.E. Hochstenbach
Defended May 28, 2003
May 2003, Utrecht University

Proceedings

(reverse chronological order)
P-10 A. Lutowska, M.E. Hochstenbach, W.H.A. Schilders
Model Order Reduction for Complex High-Tech Systems
In: B.L. Michielsen, J.-R. Poirier (Eds.), Scientific Computing in Electrical Engineering SCEE 2010, Mathematics in Industry 16, 433-441, Springer Berlin 2012 (preprint)
P-9 P. Benner, M.E. Hochstenbach, P. Kuerschner,
Two-sided harmonic subspace extractions for the generalized eigenvalue problem
Proceedings in Applied Mathematics and Mechanics 11 (1), December 2011 (preprint)
P-8 P. Benner, M.E. Hochstenbach, P. Kuerschner,
Model order reduction of large-scale dynamical systems with Jacobi-Davidson style eigensolvers
Proceedings of the IEEE International Conference on Communications, Computing and Control Applications (CCCA’11), March 2011 (preprint)
P-7 M. Patricio, M.E. Hochstenbach
An iterative method for the prediction of crack propagation on highly heterogeneous media
Proceedings of the 18th European Conference on Fracture, 2010
P-6 C. Archer, M.E. Hochstenbach, C. Hoede, G. Meinsma, H. Meijer, A.A. Salah, C.C. Stolk, T. Swist, J. Zyprych
Neural spike sorting with spatio-temporal features
In: O. Bokhove, et al. (Eds.), Proceedings of the sixty-third European Study Group Mathematics with Industry, 21-45, 2008.
P-5 E. Cator, T.J. Dijkema, M.E. Hochstenbach, W. Mulckhuyse, M. Peletier, G. Prokert, W. van der Weij, D. Worm
A sampling problem from lithography for chip layout
In: Proceedings of the fifty-eighth European study group with industry, 2007.
P-4 C. Archer, A. Hill, M.E. Hochstenbach, I. Smeets, F.P.H. van Beckum
Radioactive needlework
In: Proceedings of the fifty-fifth European study group with industry, 2006
P-3 P. van Blokland, L. Booth, K. Hiremath, M.E. Hochstenbach, G. Koole, S. Pop, M. Quant, D. Wirosoetisno
The Euro Diffusion Project
In: Proceedings of the forty-second European study group with industry, CWI Syllabus 51, 41-57 (pdf) (ESGI42), October 2002 ( bibtex )
P-2 E. Cahyono, M.E. Hochstenbach, J. Molenaar, W. Schilders, G. Terra
Velocity estimation in mixtures using tomography
In: Proceedings of the Thirty-ninth European Study Group with Industry (ESGI39), April 2001
P-1 W. J. Grootjans, M.E. Hochstenbach, J. Hurink, W. Kern, M. Luczak, Q. Puite, J. Resing, F. Spieksma
Cache as cash can
In: Proceedings of the Thirty-sixth European Study Group with Industry (ESGI36), TU Eindhoven, July 2000 ( pdf )

Book

M.E. Hochstenbach
Transition Guide from sixth to seventh edition
for Calculus, A Complete Course, by Robert A. Adams and Christopher Essex, Pearson, Toronto, 2010

Various (popularizing math, etc)

(reverse chronological order)
V-4 M.E. Hochstenbach
Eurodiffusie (Dutch)
Nieuw Archief voor de Wiskunde, March 2003
Short version in Kennislink
V-3 P. van Blokland, L. Booth, K. Hiremath, M.E. Hochstenbach, G. Koole, S. Pop, M. Quant, D. Wirosoetisno
Euro Diffusion
Vakidioot Utrecht University, August 2002
V-2 M.E. Hochstenbach, R.D. van der Meij, Q. Puite
World Wide Wait - ruimtelijke ordening op internet (Dutch)
Natuur & Techniek, February 2001
V-1 M.E. Hochstenbach, R.D. van der Meij
Caching op het Internet (Dutch)
Vakidioot Utrecht University, July 2000
Michiel Hochstenbach
Email: (m.e.hochstenbach tue nl)