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TU Berlin

Inhalt des Dokuments

Publications

Books

  • Krylov Subspace Methods. Principles and Analysis
    with Zdenek Strakos,
    Oxford University Press, 2013 (hardcover) and 2015 (paperback).

    Reviews in journals:
    Mark Embree (Bulletin of the AMS) [1]
    Martin van Gijzen (SIAM Review)
    [2]Anne Greenbaum (LAA)

    Further comments and reviews:
    Ludwig Elsner (Zentralblatt Mathematik [3])
    Melina Freitag (MathSciNet) [4]
    Nick Higham (Twitter)
    [5]
    Errata [6] (Version of 05.01.2016)

  • Linear Algebra [7]
    with Volker Mehrmann,
    Springer Undergraduate Texts in Mathematics, 2015.
    Book website at MathWorks [8]
    Zentralblatt Mathematik review [9]

  • Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis [10]
    3. durchgesehene und ergänzte Auflage,
    mit Volker Mehrmann,
    Springer-Spektrum, 2021.

  • Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis [11]
    2. überarbeitete Auflage,
    mit Volker Mehrmann,
    Springer-Spektrum, 2015.
    PaperHive Diskussion dieses Buches [12] (enthält Korrekturen und Kommentare)

  • Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis [13]
    mit Volker Mehrmann,
    Vieweg+Teubner Verlag, 2011.
    Errata [14] (Stand: 02.06.2014)
    Zentralblatt Mathematik review [15]

  • From Past to Future: Grassmann's Work in Context [16]
    H.-J. Petsche, A. C. Lewis, J. Liesen, and S. Russ, eds.,
    Birkhäuser, Basel, 2011.

Recent Publications and Preprints

  • On non-Hermitian positive (semi)definite linear algebraic systems arising from dissipative Hamiltonian DAEs [17]
    with Candan Güdücü, Volker Mehrmann and Daniel B. Szyld


  • Analysis of the multiplicative Schwarz method for matrices with a special block structure [18]
    with Carlos Echeverría and Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 54, pp. 31-50, 2021.

  • Centrality of nodes in Federated Byzantine Agreement Sytems [19]
    with André Gaul
  • Mathematical Analysis and Algorithms for Federated Byzantine Agreement Systems [20]
    with André Gaul, Ismail Khoffi and Torsten Stüber

Book Chapters

  • Matrix polynomials [21]
    with Christian Mehl,
    in Handbook of Linear Algebra, 2nd ed., Leslie Hogben ed., Chapman and Hall/CRC, Boca Raton, FL, 2014.

  • How math reduces noise [22]
    with Christian Mehl, Volker Mehrmann and Reinhard Nabben,
    in MATHEON - Mathematics for Key Technologies, Peter Deuflhard et al. eds., EMS Publishing House, 2014, pp. 226-227.

  • Hermann Grassmann's theory of linear transformations
    [23]
    in From Past to Future: Grassmann's Work in Context [24]
    H.-J. Petsche, A. C. Lewis, J. Liesen, and S. Russ, eds.,
    Birkhäuser, Basel, 2011, pp. 311-323.

Journal Publications

  • Block diagonal dominance of matrices revisited: bounds for the norms of inverses and eigenvalue inclusion sets [25]
    with Carlos Echeverria and Reinhard Nabben,
    Linear Algebra and Its Applications, vol. 553, pp. 365-383, 2018.
    BibTeX [26], arXiv version [27]

  • The maximum number of zeros of r(z)-conj{z} revisited [28]
    with Jan Zur,
    Computational Methods and Function Theory, vol. 18, no. 3, pp. 463-472, 2018.
    BibTeX [29], arXiv version [30]

  • How constant shifts affect the zeros of certain rational harmonic functions [31]
    with Jan Zur,
    Computational Methods and Function Theory, vol. 18, no. 4, pp. 583-607, 2018.
    BibTeX [32], arXiv version

    [33]
  • Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh
    [34]with Carlos Echeverria, Daniel B. Szyld, and Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 48, pp. 40-62, 2018.
    BibTeX [35]

  • Fast and accurate computation of the logarithmic capacity of compact sets [36]
    with Olivier Sete and Mohamed M. S. Nasser,
    Computational Methods and Function Theory, vol. 17, no. 4, pp. 689-713, 2017.
    BibTeX [37], arXiv version [38].

  • Properties and examples of Faber-Walsh polynomials [39]
    with Olivier Sete,
    Computational Methods and Function Theory, vol. 17, no. 1, pp. 151-177, 2017.
    BibTeX [40], arXiv version [41].

  • Using separable non-negative matrix factorization techniques for the analysis of time-resolved Raman spectra [42]
    with Robert Luce, Peter Hildebrandt and Uwe Kuhlmann,
    Applied Spectroscopy, vol. 70, no. 9, pp. 1464-1475, 2016.
    arXiv version [43].

  • Numerical computation of the conformal map onto lemniscatic domains [44]
    with Mohamed M. S. Nasser and Olivier Sete,
    Computational Methods and Function Theory, vol. 16, no. 4, pp. 609-635, 2016.
    BibTeX [45], arXiv version [46]

  • On conformal maps from multiply-connected domains onto lemniscatic domains [47]
    with Olivier Sete,
    Electronic Transactions on Numerical Analysis, vol. 45, pp. 1-15, 2016.
    BibTeX [48]

  • Fast recovery and approximation of hidden Cauchy structure [49]
    with Robert Luce,
    Linear Algebra and Its Applications, vol. 493, pp. 261-280, 2016.
    BibTeX [50], arXiv version [51]

  • Ptak's nondiscrete induction and its application to matrix iterations [52]
    IMA Journal on Numerical Analysis, vol. 36, pp. 1242-1260, 2016.
    BibTeX [53], arXiv version

    [54]
  • A note on the maximum number of zeros of r(z)-conj{z}
    [55]with Robert Luce and Olivier Sete,
    Computational Methods and Function Theory, vol. 15, pp. 439-448, 2015.
    BibTeX [56], arXiv version

    [57]
  • Creating images by adding masses to gravitational point lenses [58]
    with Olivier Sete and Robert Luce,
    General Relativity and Gravitation, 47:42, 2015. (EDITOR'S CHOICE LETTER)
    BibTeX [59], arXiv version

    [60]
  • Perturbing rational harmonic functions by poles [61]
    with Olivier Sete and Robert Luce,
    Computational Methods and Function Theory, vol. 15, pp. 9-35, 2015.
    BibTeX [62], arXiv version [63]

  • Max-min and min-max approximation problems for normal matrices revisited [64]
    with Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 41, pp. 159-166, 2014.
    BibTeX [65]

  • Sharp parameter bounds for certain maximal point lenses [66]
    with Robert Luce and Olivier Sete,
    General Relativity and Gravitation, 46:1736, 2014. (EDITOR'S CHOICE ARTICLE)
    BibTeX [67], arXiv version [68]

  • Distribution of the discretization and algebraic error in numerical solution of partial differential equations
    [69]with Jan Papez and Zdenek Strakos,

    Linear Algebra and its Applications, vol. 449, pp. 89-114, 2014.
    BibTeX [70]

  • Properties of worst-case GMRES [71]
    with Vance Faber and Petr Tichy,
    SIAM Journal on Matrix Analysis and Applications, vol. 34, pp. 1500-1519, 2013.
    BibTeX [72], arXiv version [73]

  • Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems [74]
    with Mario Arioli, Agnieszka Miedlar and Zdenek Strakos,
    GAMM Mitteilungen, vol. 36, pp. 102-129, 2013.
    BibTeX [75]

  • A framework for deflated and augmented Krylov subspace methods [76]
    with Andre Gaul, Martin H. Gutknecht and Reinhard Nabben,
    SIAM Journal on Matrix Analysis and Applications, vol. 34, pp. 495-518, 2013.
    BibTeX [77], arXiv version

    [78]
  • On Chebyshev polynomials of matrices [79]
    with Vance Faber and Petr Tichy,
    SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 2205-2221, 2010.
    BibTeX [80]

  • On best approximations of polynomials in matrices in the matrix 2-norm [81]
    with Petr Tichy,
    SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 853-863, 2009.
    BibTeX [82]

  • On orthogonal reduction to Hessenberg form with small bandwidth [83]
    with Vance Faber and Petr Tichy,
    Numerical Algorithms, vol. 51, pp. 133-142, 2009.
    BibTeX [84]

  • On optimal short recurrences for generating orthogonal Krylov subspace bases [85]
    with Zdenek Strakos,
    SIAM Review, vol. 50, pp. 485-503, 2008.
    BibTeX [86]

  • On nonsymmetric saddle point matrices that allow conjugate gradient iterations [87]
    with Beresford Parlett,
    Numerische Mathematik, vol. 108, pp. 605-624, 2008.
    BibTeX [88]

  • The Faber-Manteuffel Theorem for linear operators [89]
    with Vance Faber and Petr Tichy,
    SIAM Journal on Numerical Analysis, vol. 46, pp. 1323-1337, 2008.
    BibTeX [90]

  • On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block [91]
    with Petr Tichy and Vance Faber,
    Electronic Transactions on Numerical Analysis, vol. 26, pp. 453-473, 2007.
    BibTeX [92]

  • When is the adjoint of a matrix a low degree rational function in the matrix? [93]
    SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 4, pp. 1171-1180, 2007.
    BibTeX [94]

  • Numerical solution of saddle point problems [95]
    with Michele Benzi and Gene H. Golub,
    Acta Numerica, vol. 14, pp. 1-137, 2005.
    BibTeX [96]

  • GMRES convergence analysis for a convection-diffusion model problem [97]
    with Zdenek Strakos,
    SIAM Journal on Scientific Computing, vol. 26, no. 6, pp. 1989-2009, 2005.
    BibTeX [98]

  • Block-diagonal and constraint preconditioners for nonsymmetric indefinite linear systems. Part I: Theory [99]
    with Eric de Sturler,
    SIAM Journal on Scientific Computing, vol. 26, no. 5, pp. 1598-1619, 2005.
    BibTeX [100]

  • On numerical stability in large scale linear algebraic computations [101]
    with Zdenek Strakos,
    Zeitschrift für Angewandte Mathematik und Mechanik, vol. 85, no. 5, pp. 307-325, 2005.
    BibTeX [102]

  • Orthogonal Hessenberg reduction and orthogonal Krylov subspace bases [103]
    with Paul E. Saylor,
    SIAM Journal on Numerical Analysis, vol. 42, no. 5, pp. 2148-2158, 2005.
    BibTeX [104]

  • On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toepliz matrices [105]
    with Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 20, pp. 180-197, 2005.
    BibTeX [106]

  • Convergence analysis of Krylov subspace methods [107]
    with Petr Tichy,
    GAMM Mitteilungen, vol. 27, no. 2, pp. 153-173, 2004.
    BibTeX [108]

  • Convergence of GMRES for tridiagonal Toeplitz matrices [109]
    with Zdenek Strakos,
    SIAM Journal on Matrix Analysis and Applications, vol. 26, no. 1, pp. 233-251, 2004.
    BibTeX [110]

  • The worst-case GMRES for normal matrices [111]
    with Petr Tichy,
    BIT, vol. 44, no. 1, pp. 79-98, 2004.
    BibTeX [112]

  • Least squares residuals and minimal residual methods [113]
    with Miro Rozloznik and Zdenek Strakos,
    SIAM Journal on Scientific Computing, vol. 23, no. 5, pp. 1503-1525, 2002.
    BibTeX [114]

  • Faber polynomials corresponding to rational exterior mapping functions [115]
    Constructive Approximation, vol. 17, no. 2, pp. 267-274, 2001.
    BibTeX [116]

  • On the location of the zeros of Faber polynomials [117]
    Analysis, vol. 20, no. 2, pp. 157-162, 2000.
    BibTeX [118]

  • Computable convergence bounds for GMRES [119]
    SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 3, pp. 882-903, 2000.
    BibTeX [120]

  • The conformal 'bratwurst' maps and associated Faber polynomials [121]
    with Tino Koch,
    Numerische Mathematik, vol. 86, pp. 173-191, 2000.
    BibTeX
    [122]

Further Publications

  • Preface LAA Special Issue on Matrix Functions [123]
    with Oliver G. Ernst, Chun-Hua Guo and Leiba Rodman
    Linear Algebra and Its Applications, vol. 456, pp. 1-2, 2014.

  • The field of values bound on ideal GMRES [124]
    with Petr Tichy,
    arXiv:1211.5969, 2012.

  • Analysis of the second phase of the GMRES convergence for a convection-diffusion model problem [125]
    with Jurjen Duintjer-Tebbens and Zdenek Strakos,
    Preprint 861, DFG Research Center Matheon, 2012.
  • Deflated and augmented Krylov subspace methods: Basic facts and a breakdown-free deflated MINRES [126]
    with Andre Gaul, Martin H. Gutknecht and Reinhard Nabben,
    Preprint 759, DFG Research Center Matheon, 2011.

  • On the factorization of Simplex basis matrices [127]
    with Robert Luce et al.
    Zuse Institute Berlin, ZIB-Report 09-24, 2009.

  • Householder XVI: Numerical Linear Algebra on the Lake [128]
    with Volker Mehrmann and Reinhard Nabben
    SIAM News, October 2008.

  • GMRES convergence and the polynomial numerical hull for a Jordan block [129] [130]
    with Petr Tichy,
    Preprint 34-2006, Institute of Mathematics, TU Berlin, 2006
    (preliminary version of the paper with P. Tichy and V. Faber that appeared in ETNA).

  • Behavior of CG and MINRES for symmetric tridiagonal Toeplitz matrices [131]
    with Petr Tichy,
    Preprint 34-2004, Institut of Mathematics, TU Berlin, 2004
    (contains more details on worst-case MR data for the Poisson model problem than the ETNA paper).

  • A min-max problem on roots of unity [132]
    with Petr Tichy,
    Preprint 28-2003, Institute of Mathematics, TU Berlin, 2003.

  • Convergence analysis of GMRES for the SUPG discretized convection-diffusion model problem [133] [134]
    with Zdenek Strakos,
    Preprint 26-2003, Institute of Mathematics, TU Berlin, 2003
    (contains more numerical experiments than the SISC paper).

  • Slow initial convergence of GMRES for SUPG discretized convection-diffusion problems [135]
    with Zdenek Strakos,
    Proceedings in Applied Mathematics and Mechanics, vol. 3, no. 1, pp. 551-552, 2003.

  • Preconditioners for indefinite linear systems arising in surface parameterization [136]
    with Eric de Sturler, Alla Sheffa, Yelda Aydin, and Chris Siefert,
    Proceedings of the 10th Internatinal Meshing Roundtable (Newport Beach, CA, USA, October 7-10, 2001), Sandia National Laboratories, pp. 71-81, 2001.

  • Construction and analysis of polynomial iterative methods for non-hermitian systems of linear equations [137]
    Dissertation, Department of Mathematics, University of Bielefeld, November 1998.
Lupe [138]
Lupe [139]
Lupe [140]
Lupe [141]
Lupe [142]
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