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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]
    2. überarbeitete Auflage,
    mit Volker Mehrmann,
    Springer-Spektrum, 2015.
    PaperHive Diskussion dieses Buches [11] (enthält Korrekturen und Kommentare)

  • Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis [12]
    mit Volker Mehrmann,
    Vieweg+Teubner Verlag, 2011.
    Errata [13] (Stand: 02.06.2014)
    Zentralblatt Mathematik review [14]

  • From Past to Future: Grassmann's Work in Context [15]
    H.-J. Petsche, A. C. Lewis, J. Liesen, and S. Russ, eds.,
    Birkhäuser, Basel, 2011.

Recent Publications and Preprints

  • Analysis of the multiplicative Schwarz method for matrices with a special block structure [16]
    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 [17]
    with André Gaul
  • Mathematical Analysis and Algorithms for Federated Byzantine Agreement Systems [18]
    with André Gaul, Ismail Khoffi and Torsten Stüber

Book Chapters

  • Matrix polynomials [19]
    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 [20]
    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
    [21]     in From Past to Future: Grassmann's Work in Context [22]
    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 [23]
    with Carlos Echeverria and Reinhard Nabben,
    Linear Algebra and Its Applications, vol. 553, pp. 365-383, 2018.
    BibTeX [24], arXiv version [25]

  • The maximum number of zeros of r(z)-conj{z} revisited [26]
    with Jan Zur,
    Computational Methods and Function Theory, vol. 18, no. 3, pp. 463-472, 2018.
    BibTeX [27], arXiv version [28]

  • How constant shifts affect the zeros of certain rational harmonic functions [29]
    with Jan Zur,
    Computational Methods and Function Theory, vol. 18, no. 4, pp. 583-607, 2018.
    BibTeX [30], arXiv version

    [31]
  • Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh
     [32]with Carlos Echeverria, Daniel B. Szyld, and Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 48, pp. 40-62, 2018.
    BibTeX [33]

  • Fast and accurate computation of the logarithmic capacity of compact sets [34]
    with Olivier Sete and Mohamed M. S. Nasser,
    Computational Methods and Function Theory, vol. 17, no. 4, pp. 689-713, 2017.
    BibTeX [35], arXiv version [36].

  • Properties and examples of Faber-Walsh polynomials [37]
    with Olivier Sete,
    Computational Methods and Function Theory, vol. 17, no. 1, pp. 151-177, 2017.
    BibTeX [38], arXiv version [39].

  • Using separable non-negative matrix factorization techniques for the analysis of time-resolved Raman spectra [40]
    with Robert Luce, Peter Hildebrandt and Uwe Kuhlmann,
    Applied Spectroscopy, vol. 70, no. 9, pp. 1464-1475, 2016.
    arXiv version [41].

  • Numerical computation of the conformal map onto lemniscatic domains [42]
    with Mohamed M. S. Nasser and Olivier Sete,
    Computational Methods and Function Theory, vol. 16, no. 4, pp. 609-635, 2016.
    BibTeX [43], arXiv version [44]

  • On conformal maps from multiply-connected domains onto lemniscatic domains [45]
    with Olivier Sete,
    Electronic Transactions on Numerical Analysis, vol. 45, pp. 1-15, 2016.
    BibTeX [46]

  • Fast recovery and approximation of hidden Cauchy structure [47]
    with Robert Luce,
    Linear Algebra and Its Applications, vol. 493, pp. 261-280, 2016.
    BibTeX [48], arXiv version [49]

  • Ptak's nondiscrete induction and its application to matrix iterations [50]
    IMA Journal on Numerical Analysis, vol. 36, pp. 1242-1260, 2016.
    BibTeX [51], arXiv version

    [52]
  • A note on the maximum number of zeros of r(z)-conj{z}
    [53]with Robert Luce and Olivier Sete,
    Computational Methods and Function Theory, vol. 15, pp. 439-448, 2015.
    BibTeX [54], arXiv version

    [55]
  • Creating images by adding masses to gravitational point lenses [56]
    with Olivier Sete and Robert Luce,
    General Relativity and Gravitation, 47:42, 2015. (EDITOR'S CHOICE LETTER)
    BibTeX [57], arXiv version

    [58]
  • Perturbing rational harmonic functions by poles [59]
    with Olivier Sete and Robert Luce,
    Computational Methods and Function Theory, vol. 15, pp. 9-35, 2015.
    BibTeX [60], arXiv version [61]

  • Max-min and min-max approximation problems for normal matrices revisited [62]
    with Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 41, pp. 159-166, 2014.
    BibTeX [63]

  • Sharp parameter bounds for certain maximal point lenses [64]
    with Robert Luce and Olivier Sete,
    General Relativity and Gravitation, 46:1736, 2014. (EDITOR'S CHOICE ARTICLE)
    BibTeX [65], arXiv version [66]

  • Distribution of the discretization and algebraic error in numerical solution of partial differential equations
     [67]with Jan Papez and Zdenek Strakos,
    Linear Algebra and its Applications, vol. 449, pp. 89-114, 2014.
    BibTeX [68]

  • Properties of worst-case GMRES [69]
    with Vance Faber and Petr Tichy,
    SIAM Journal on Matrix Analysis and Applications, vol. 34, pp. 1500-1519, 2013.
    BibTeX [70], arXiv version [71]

  • Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems [72]
    with Mario Arioli, Agnieszka Miedlar and Zdenek Strakos,
    GAMM Mitteilungen, vol. 36, pp. 102-129, 2013.
    BibTeX [73]

  • A framework for deflated and augmented Krylov subspace methods [74]
    with Andre Gaul, Martin H. Gutknecht and Reinhard Nabben,
    SIAM Journal on Matrix Analysis and Applications, vol. 34, pp. 495-518, 2013.
    BibTeX [75], arXiv version

    [76]
  • On Chebyshev polynomials of matrices [77]
    with Vance Faber and Petr Tichy,
    SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 2205-2221, 2010.
    BibTeX [78]

  • On best approximations of polynomials in matrices in the matrix 2-norm [79]
    with Petr Tichy,
    SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 853-863, 2009.
    BibTeX [80]

  • On orthogonal reduction to Hessenberg form with small bandwidth [81]
    with Vance Faber and Petr Tichy,
    Numerical Algorithms, vol. 51, pp. 133-142, 2009.
    BibTeX [82]

  • On optimal short recurrences for generating orthogonal Krylov subspace bases [83]
    with Zdenek Strakos,
    SIAM Review, vol. 50, pp. 485-503, 2008.
    BibTeX [84]

  • On nonsymmetric saddle point matrices that allow conjugate gradient iterations [85]
    with Beresford Parlett,
    Numerische Mathematik, vol. 108, pp. 605-624, 2008.
    BibTeX [86]

  • The Faber-Manteuffel Theorem for linear operators [87]
    with Vance Faber and Petr Tichy,
    SIAM Journal on Numerical Analysis, vol. 46, pp. 1323-1337, 2008.
    BibTeX [88]

  • On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block [89]
    with Petr Tichy and Vance Faber,
    Electronic Transactions on Numerical Analysis, vol. 26, pp. 453-473, 2007.
    BibTeX [90]

  • When is the adjoint of a matrix a low degree rational function in the matrix? [91]
    SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 4, pp. 1171-1180, 2007.
    BibTeX [92]

  • Numerical solution of saddle point problems [93]
    with Michele Benzi and Gene H. Golub,
    Acta Numerica, vol. 14, pp. 1-137, 2005.
    BibTeX [94]

  • GMRES convergence analysis for a convection-diffusion model problem [95]
    with Zdenek Strakos,
    SIAM Journal on Scientific Computing, vol. 26, no. 6, pp. 1989-2009, 2005.
    BibTeX [96]

  • Block-diagonal and constraint preconditioners for nonsymmetric indefinite linear systems. Part I: Theory [97]
    with Eric de Sturler,
    SIAM Journal on Scientific Computing, vol. 26, no. 5, pp. 1598-1619, 2005.
    BibTeX [98]

  • On numerical stability in large scale linear algebraic computations [99]
    with Zdenek Strakos,
    Zeitschrift für Angewandte Mathematik und Mechanik, vol. 85, no. 5, pp. 307-325, 2005.
    BibTeX [100]

  • Orthogonal Hessenberg reduction and orthogonal Krylov subspace bases [101]
    with Paul E. Saylor,
    SIAM Journal on Numerical Analysis, vol. 42, no. 5, pp. 2148-2158, 2005.
    BibTeX [102]

  • On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toepliz matrices [103]
    with Petr Tichy,
    Electronic Transactions on Numerical Analysis, vol. 20, pp. 180-197, 2005.
    BibTeX [104]

  • Convergence analysis of Krylov subspace methods [105]
    with Petr Tichy,
    GAMM Mitteilungen, vol. 27, no. 2, pp. 153-173, 2004.
    BibTeX [106]

  • Convergence of GMRES for tridiagonal Toeplitz matrices [107]
    with Zdenek Strakos,
    SIAM Journal on Matrix Analysis and Applications, vol. 26, no. 1, pp. 233-251, 2004.
    BibTeX [108]

  • The worst-case GMRES for normal matrices [109]
    with Petr Tichy,
    BIT, vol. 44, no. 1, pp. 79-98, 2004.
    BibTeX [110]

  • Least squares residuals and minimal residual methods [111]
    with Miro Rozloznik and Zdenek Strakos,
    SIAM Journal on Scientific Computing, vol. 23, no. 5, pp. 1503-1525, 2002.
    BibTeX [112]

  • Faber polynomials corresponding to rational exterior mapping functions [113]
    Constructive Approximation, vol. 17, no. 2, pp. 267-274, 2001.
    BibTeX [114]

  • On the location of the zeros of Faber polynomials [115]
    Analysis, vol. 20, no. 2, pp. 157-162, 2000.
    BibTeX [116]

  • Computable convergence bounds for GMRES [117]
    SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 3, pp. 882-903, 2000.
    BibTeX [118]

  • The conformal 'bratwurst' maps and associated Faber polynomials [119]
    with Tino Koch,
    Numerische Mathematik, vol. 86, pp. 173-191, 2000.
    BibTeX
    [120]

Further Publications

  • Preface LAA Special Issue on Matrix Functions [121]
    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 [122]
    with Petr Tichy,
    arXiv:1211.5969, 2012.

  • Analysis of the second phase of the GMRES convergence for a convection-diffusion model problem [123]
    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 [124]
    with Andre Gaul, Martin H. Gutknecht and Reinhard Nabben,
    Preprint 759, DFG Research Center Matheon, 2011.

  • On the factorization of Simplex basis matrices [125]
    with Robert Luce et al.
    Zuse Institute Berlin, ZIB-Report 09-24, 2009.

  • Householder XVI: Numerical Linear Algebra on the Lake [126]
    with Volker Mehrmann and Reinhard Nabben
    SIAM News, October 2008.

  • GMRES convergence and the polynomial numerical hull for a Jordan block [127] [128]
    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 [129]
    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 [130]
    with Petr Tichy,
    Preprint 28-2003, Institute of Mathematics, TU Berlin, 2003.

  • Convergence analysis of GMRES for the SUPG discretized convection-diffusion model problem [131] [132]
    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 [133]
    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 [134]
    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 [135]
    Dissertation, Department of Mathematics, University of Bielefeld, November 1998.
Lupe [136]
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