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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)
Martin van Gijzen (SIAM Review)
Anne Greenbaum (LAA)
Further comments and reviews:
Ludwig Elsner (Zentralblatt Mathematik)
Melina Freitag (MathSciNet)
Nick Higham (Twitter)
Errata (Version of 05.01.2016) - Linear Algebra
with Volker Mehrmann,
Springer Undergraduate Texts in Mathematics, 2015.
Book website at MathWorks
Zentralblatt Mathematik review - Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis
2. überarbeitete Auflage,
mit Volker Mehrmann,
Springer-Spektrum, 2015.
PaperHive Diskussion dieses Buches (enthält Korrekturen und Kommentare) - Lineare Algebra. Ein Lehrbuch über die Theorie mit Blick auf die Praxis
mit Volker Mehrmann,
Vieweg+Teubner Verlag, 2011.
Errata (Stand: 02.06.2014)
Zentralblatt Mathematik review - From Past to Future: Grassmann's Work in Context
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
with Carlos Echeverría and Petr Tichy
- Mathematical Analysis and Algorithms for Federated Byzantine Agreement Systems
with André Gaul, Ismail Khoffi and Torsten Stüber
Book Chapters
- Matrix polynomials
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
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
in From Past to Future: Grassmann's Work in Context
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
with Carlos Echeverria and Reinhard Nabben,
Linear Algebra and Its Applications, vol. 553, pp. 365-383, 2018.
BibTeX, arXiv version - The maximum number of zeros of r(z)-\conj{z} revisited
with Jan Zur,
Computational Methods and Function Theory, vol. 18, no. 3, pp. 463-472, 2018.
BibTeX, arXiv version - How constant shifts affect the zeros of certain rational harmonic functions
with Jan Zur,
Computational Methods and Function Theory, vol. 18, no. 4, pp. 583-607, 2018.
BibTeX, arXiv version - Convergence of the multiplicative Schwarz method for singularly perturbed convection-diffusion problems discretized on a Shishkin mesh
with Carlos Echeverria, Daniel B. Szyld, and Petr Tichy,
Electronic Transactions on Numerical Analysis, vol. 48, pp. 40-62, 2018.
BibTeX - Fast and accurate computation of the logarithmic capacity of compact sets
with Olivier Sete and Mohamed M. S. Nasser,
Computational Methods and Function Theory, vol. 17, no. 4, pp. 689-713, 2017.
BibTeX, arXiv version. - Properties and examples of Faber-Walsh polynomials
with Olivier Sete,
Computational Methods and Function Theory, vol. 17, no. 1, pp. 151-177, 2017.
BibTeX, arXiv version. - Using separable non-negative matrix factorization techniques for the analysis of time-resolved Raman spectra
with Robert Luce, Peter Hildebrandt and Uwe Kuhlmann,
Applied Spectroscopy, vol. 70, no. 9, pp. 1464-1475, 2016.
arXiv version. - Numerical computation of the conformal map onto lemniscatic domains
with Mohamed M. S. Nasser and Olivier Sete,
Computational Methods and Function Theory, vol. 16, no. 4, pp. 609-635, 2016.
BibTeX, arXiv version - On conformal maps from multiply-connected domains onto lemniscatic domains
with Olivier Sete,
Electronic Transactions on Numerical Analysis, vol. 45, pp. 1-15, 2016.
BibTeX - Fast recovery and approximation of hidden Cauchy structure
with Robert Luce,
Linear Algebra and Its Applications, vol. 493, pp. 261-280, 2016.
BibTeX, arXiv version - Ptak's nondiscrete induction and its application to matrix iterations
IMA Journal on Numerical Analysis, vol. 36, pp. 1242-1260, 2016.
BibTeX, arXiv version - A note on the maximum number of zeros of r(z)-\conj{z}
with Robert Luce and Olivier Sete,
Computational Methods and Function Theory, vol. 15, pp. 439-448, 2015.
BibTeX, arXiv version - Creating images by adding masses to gravitational point lenses
with Olivier Sete and Robert Luce,
General Relativity and Gravitation, 47:42, 2015. (EDITOR'S CHOICE LETTER)
BibTeX, arXiv version - Perturbing rational harmonic functions by poles
with Olivier Sete and Robert Luce,
Computational Methods and Function Theory, vol. 15, pp. 9-35, 2015.
BibTeX, arXiv version - Max-min and min-max approximation problems for normal matrices revisited
with Petr Tichy,
Electronic Transactions on Numerical Analysis, vol. 41, pp. 159-166, 2014.
BibTeX - Sharp parameter bounds for certain maximal point lenses
with Robert Luce and Olivier Sete,
General Relativity and Gravitation, 46:1736, 2014. (EDITOR'S CHOICE ARTICLE)
BibTeX, arXiv version - Distribution of the discretization and algebraic error in numerical solution of partial differential equations
with Jan Papez and Zdenek Strakos,
Linear Algebra and its Applications, vol. 449, pp. 89-114, 2014.
BibTeX - Properties of worst-case GMRES
with Vance Faber and Petr Tichy,
SIAM Journal on Matrix Analysis and Applications, vol. 34, pp. 1500-1519, 2013.
BibTeX, arXiv version - Interplay between discretization and algebraic computation in adaptive numerical solution of elliptic PDE problems
with Mario Arioli, Agnieszka Miedlar and Zdenek Strakos,
GAMM Mitteilungen, vol. 36, pp. 102-129, 2013.
BibTeX - A framework for deflated and augmented Krylov subspace methods
with Andre Gaul, Martin H. Gutknecht and Reinhard Nabben,
SIAM Journal on Matrix Analysis and Applications, vol. 34, pp. 495-518, 2013.
BibTeX, arXiv version - On Chebyshev polynomials of matrices
with Vance Faber and Petr Tichy,
SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 2205-2221, 2010.
BibTeX - On best approximations of polynomials in matrices in the matrix 2-norm
with Petr Tichy,
SIAM Journal on Matrix Analysis and Applications, vol. 31, pp. 853-863, 2009.
BibTeX - On orthogonal reduction to Hessenberg form with small bandwidth
with Vance Faber and Petr Tichy,
Numerical Algorithms, vol. 51, pp. 133-142, 2009.
BibTeX - On optimal short recurrences for generating orthogonal Krylov subspace bases
with Zdenek Strakos,
SIAM Review, vol. 50, pp. 485-503, 2008.
BibTeX - On nonsymmetric saddle point matrices that allow conjugate gradient iterations
with Beresford Parlett,
Numerische Mathematik, vol. 108, pp. 605-624, 2008.
BibTeX - The Faber-Manteuffel Theorem for linear operators
with Vance Faber and Petr Tichy,
SIAM Journal on Numerical Analysis, vol. 46, pp. 1323-1337, 2008.
BibTeX - On worst-case GMRES, ideal GMRES, and the polynomial numerical hull of a Jordan block
with Petr Tichy and Vance Faber,
Electronic Transactions on Numerical Analysis, vol. 26, pp. 453-473, 2007.
BibTeX - When is the adjoint of a matrix a low degree rational function in the matrix?
SIAM Journal on Matrix Analysis and Applications, vol. 29, no. 4, pp. 1171-1180, 2007.
BibTeX - Numerical solution of saddle point problems
with Michele Benzi and Gene H. Golub,
Acta Numerica, vol. 14, pp. 1-137, 2005.
BibTeX - GMRES convergence analysis for a convection-diffusion model problem
with Zdenek Strakos,
SIAM Journal on Scientific Computing, vol. 26, no. 6, pp. 1989-2009, 2005.
BibTeX - Block-diagonal and constraint preconditioners for nonsymmetric indefinite linear systems. Part I: Theory
with Eric de Sturler,
SIAM Journal on Scientific Computing, vol. 26, no. 5, pp. 1598-1619, 2005.
BibTeX - On numerical stability in large scale linear algebraic computations
with Zdenek Strakos,
Zeitschrift für Angewandte Mathematik und Mechanik, vol. 85, no. 5, pp. 307-325, 2005.
BibTeX - Orthogonal Hessenberg reduction and orthogonal Krylov subspace bases
with Paul E. Saylor,
SIAM Journal on Numerical Analysis, vol. 42, no. 5, pp. 2148-2158, 2005.
BibTeX - On the worst-case convergence of MR and CG for symmetric positive definite tridiagonal Toepliz matrices
with Petr Tichy,
Electronic Transactions on Numerical Analysis, vol. 20, pp. 180-197, 2005.
BibTeX - Convergence analysis of Krylov subspace methods
with Petr Tichy,
GAMM Mitteilungen, vol. 27, no. 2, pp. 153-173, 2004.
BibTeX - Convergence of GMRES for tridiagonal Toeplitz matrices
with Zdenek Strakos,
SIAM Journal on Matrix Analysis and Applications, vol. 26, no. 1, pp. 233-251, 2004.
BibTeX - The worst-case GMRES for normal matrices
with Petr Tichy,
BIT, vol. 44, no. 1, pp. 79-98, 2004.
BibTeX - Least squares residuals and minimal residual methods
with Miro Rozloznik and Zdenek Strakos,
SIAM Journal on Scientific Computing, vol. 23, no. 5, pp. 1503-1525, 2002.
BibTeX - Faber polynomials corresponding to rational exterior mapping functions
Constructive Approximation, vol. 17, no. 2, pp. 267-274, 2001.
BibTeX - On the location of the zeros of Faber polynomials
Analysis, vol. 20, no. 2, pp. 157-162, 2000.
BibTeX - Computable convergence bounds for GMRES
SIAM Journal on Matrix Analysis and Applications, vol. 21, no. 3, pp. 882-903, 2000.
BibTeX - The conformal 'bratwurst' maps and associated Faber polynomials
with Tino Koch,
Numerische Mathematik, vol. 86, pp. 173-191, 2000.
BibTeX
Further Publications
- Preface LAA Special Issue on Matrix Functions
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
with Petr Tichy,
arXiv:1211.5969, 2012. - Analysis of the second phase of the GMRES convergence for a convection-diffusion model problem
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
with Andre Gaul, Martin H. Gutknecht and Reinhard Nabben,
Preprint 759, DFG Research Center Matheon, 2011. - On the factorization of Simplex basis matrices
with Robert Luce et al.
Zuse Institute Berlin, ZIB-Report 09-24, 2009. - Householder XVI: Numerical Linear Algebra on the Lake
with Volker Mehrmann and Reinhard Nabben
SIAM News, October 2008. - GMRES convergence and the polynomial numerical hull for a Jordan block
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
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
with Petr Tichy,
Preprint 28-2003, Institute of Mathematics, TU Berlin, 2003. - Convergence analysis of GMRES for the SUPG discretized convection-diffusion model problem
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
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
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
Dissertation, Department of Mathematics, University of Bielefeld, November 1998.
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