Publications of Christian Mehl

  
Disclaimer:
 
The files offered for download on this page are preliminary or preprint versions if not stated otherwise. The download is permitted for scholary purposes only. The links to the final versions of the articles are external links. A subscription to the corresponding journal may be necessary to be able to view the article.
 
Table of contents:
 
Accepted or Submitted for Publication: (in reverse chronological order)
 
  1. Michiel Hochstenbach, Christian Mehl, Bor Plestenjak.
    Numerical methods for eigenvalues of singular polynomial eigenvalue problems.
    Submitted for publication, 2024.
    ArXiv-Preprint.
     
  2. Michiel Hochstenbach, Christian Mehl, Bor Plestenjak.
    Solving singular generalized eigenvalue problems. Part III: structure preservation.
    Submitted for publication, 2024.
    ArXiv-Preprint.
     
  3. Christian Mehl, Volker Mehrmann, Michał Wojtylak.
    Spectral theory of infinite dimensional dissipative Hamiltonian systems.
    Submitted for publication, 2024.
    ArXiv-Preprint.
 
Refereed Research Articles: (in reverse chronological order)
 
  1. Fredy Sosa, Julio Moro, Christian Mehl.
    First order structure-preserving perturbation theory for eigenvalues of symplectic matrices: Part II.
    Linear Algebra Appl., 689:196-229, 2024.
    Article: http://dx.doi.org/10.1016/j.laa.2024.02.018.
     
  2. Michiel Hochstenbach, Christian Mehl, Bor Plestenjak.
    Solving singular generalized eigenvalue problems. Part II: projection and augmentation.
    SIAM J. Matrix Anal. Appl, 44:1589-1618, 2023.
    ArXiv-Preprint, Article: http://dx.doi.org/10.1137/22M1513174.
     
  3. Christian Mehl, Volker Mehrmann, Michał Wojtylak.
    Matrix pencils with coefficients that have positive semidefinite Hermitian part.
    SIAM J. Matrix Anal. Appl., 43:1186-1212, 2022.
    ArXiv-Preprint, Article: http://dx.doi.org/10.1137/21M1439997.
     
  4. Fernando De Téran, Christian Mehl, Volker Mehrmann
    Low rank perturbation of regular matrix pencils with symmetry structures .
    Found. Comput. Math., 22:257-311, 2022.
    Preprint, Article: http://dx.doi.org/10.1007/s10208-021-09500-4.
     
  5. Christian Mehl, Volker Mehrmann, Michał Wojtylak
    Distance problems for dissipative Hamiltonian systems and related matrix polynomials.
    Linear Algebra Appl., 623:335-366, 2021.
    Preprint, Article: http://dx.doi.org/10.1016/j.laa.2020.05.026.
     
  6. Christian Mehl
    On the existence of Schur-like forms for matrices with symmetry structures.
    Vietnam Journal of Mathematics, 48:831-845, 2020.
    pdf-file, Article: https://doi.org/10.1007/s10013-020-00394-3.
     
  7. Fredy Sosa, Julio Moro, Christian Mehl.
    First order structure-preserving perturbation theory for eigenvalues of symplectic matrices.
    SIAM J. Matrix Anal. Appl., 41:657-690, 2020.
    Preprint, Article: https://doi.org/10.1137/17M1124723.
     
  8. Michiel Hochstenbach, Christian Mehl, Bor Plestenjak
    Solving singular generalized eigenvalue problems by a rank-completing perturbation.
    SIAM J. Matrix Anal. Appl., 40:1022-1046, 2019.
    Preprint, Article: https://doi.org/10.1137/18M1188628.
     
  9. Christian Mehl, Volker Mehrmann, Punit Sharma.
    Structured eigenvalue/eigenvector backward errors of matrix pencils arising in optimal control.
    Electron. J. Linear Algebra, 34:526-560, 2018.
    Preprint, Article: http://doi.org/10.13001/1081-3810.3687.
     
  10. Christian Mehl, Volker Mehrmann, Michał Wojtylak
    Linear algebra properties of dissipative Hamiltonian descriptor systems.
    SIAM Matrix Anal. Appl., 39:1489-1519, 2018.
    Preprint, Article: http://doi.org/10.1137/18M1164275.
     
  11. Christian Mehl, André Ran.
    Low rank perturbation of quaternion matrices.
    Electron. J. Linear Algebra, 32: 514-530, 2017.
    Preprint, Article: http://doi.org/10.13001/1081-3810.3629.
     
  12. Christian Mehl, Volker Mehrmann, Punit Sharma.
    Stability radii for real linear Hamiltonian systems with perturbed dissipation.
    BIT, 57:811-843, 2017.
    pdf-file. Article: http://dx.doi.org/10.1007/s10543-017-0654-0.
     
  13. Christian Mehl, Volker Mehrmann, Michał Wojtylak.
    Parameter-dependent rank-one perturbations of singular Hermitian or symmetric pencils.
    SIAM J. Matrix Anal. Appl., 38:72-95, 2017.
    pdf-file. Article: http://dx.doi.org/10.1137/16M1060352.
     
  14. Christian Mehl, Volker Mehrmann, Punit Sharma.
    Stability radii for linear Hamiltonian systems with dissipation under structure-preserving perturbations.
    SIAM J. Matrix Anal. Appl., 37:1625-1654, 2016.
    pdf-file. Article: http://dx.doi.org/10.1137/16M1067330.
     
  15. Leonhard Batzke, Christian Mehl, André C.M. Ran, Leiba Rodman.
    Generic rank-k perturbations of structured matrices.
    Oper. Theory Adv. Appl., 255:27-48, 2016.
    pdf-file, Article: http://dx.doi.org/10.1007/978-3-319-31383-2_2.
     
  16. Christian Mehl, Volker Mehrmann, André C.M. Ran, Leiba Rodman.
    Eigenvalue perturbation theory of structured real matrices and their sign characteristics under generic structured rank-one perturbations.
    Linear and Multilinear Algebra, 64: 527-556, 2016.
    pdf-file, Article: http://dx.doi.org/10.1080/03081087.2015.1053425.
     
  17. Christian Mehl, Volker Mehrmann, Michał Wojtylak.
    On the distance to singularity via low rank perturbations.
    Oper. Matrices, 9:733-772, 2015.
    pdf-file, Article: http://dx.doi.org/10.7153/oam-09-44.
     
  18. Shreemayee Bora, Michael Karow, Christian Mehl, Punit Sharma.
    Structured eigenvalue backward errors of matrix pencils and polynomials with palindromic structures.
    SIAM J. Matrix Anal. Appl., 36:393-416, 2015.
    pdf-file, Article: http://dx.doi.org/10.1137/140973839.
     
  19. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Möbius transformations of matrix polynomials.
    Linear Algebra Appl., 470:120-184, 2015.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2014.05.013.
     
  20. Shreemayee Bora, Michael Karow, Christian Mehl, Punit Sharma.
    Structured eigenvalue backward errors of matrix pencils and polynomials with Hermitian and related structures.
    SIAM J. Matrix Anal. Appl., 35:453-475, 2014.
    pdf-file, Article: http://dx.doi.org/10.1137/130925621.
     
  21. Leonhard Batzke, Christian Mehl.
    On the inverse eigenvalue problem for T-alternating and T-palindromic matrix polynomials.
    Linear Algebra Appl., 452:172-191, 2014.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2014.03.037.
     
  22. Christian Mehl, Volker Mehrmann, André C.M. Ran, Leiba Rodman.
    Eigenvalue perturbation theory of symplectic, orthogonal, and unitary matrices under generic structured rank one perturbations.
    BIT, 54:219-255, 2014.
    pdf-file, Article: http://dx.doi.org/10.1007/s10543-013-0451-3.
     
  23. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Skew-symmetric matrix polynomials and their Smith forms.
    Linear Algebra Appl., 438:4625-4653, 2013.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2013.02.010.
     
  24. Christian Mehl, Volker Mehrmann, André C.M. Ran, Leiba Rodman.
    Jordan forms of real and complex matrices under rank one perturbations.
    Oper. Matrices, 7:381-398, 2013.
    pdf-file, Article: http://dx.doi.org/10.7153/oam-07-22.
     
  25. Christian Mehl, Volker Mehrmann, André C.M. Ran, Leiba Rodman.
    Perturbation theory of selfadjoint matrices and sign characteristics under generic structured rank one perturbations.
    Linear Algebra Appl., 436:4027-4042, 2012.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2010.04.008.
     
  26. Christian Mehl, Volker Mehrmann, André C.M. Ran, Leiba Rodman.
    Eigenvalue perturbation theory of classes of structured matrices under generic structured rank one perturbations.
    Linear Algebra Appl., 435:687-716, 2011.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2010.07.025.
     
  27. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Smith forms of palindromic matrix polynomials.
    Electron. J. Linear Algebra, 22:53-91, 2011.
    pdf-file, Article: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol22_pp53-91.pdf.
     
  28. Mark-Alexander Henn, Christian Mehl, Carsten Trunk.
    Hyponormal and strongly hyponormal matrices in inner product spaces.
    Linear Algebra Appl., 433:1055-1076, 2010.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2010.04.050.
     
  29. Nicholas J. Higham, Christian Mehl, Françoise Tisseur.
    The canonical generalized polar decomposition.
    SIAM J. Matrix Anal. Appl., 31:2163-2180, 2010.
    pdf-file, Article: http://dx.doi.org/10.1137/090765018.
     
  30. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Jordan structures of alternating matrix polynomials.
    Linear Algebra Appl., 432:867-891, 2010.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2009.10.002.
     
  31. Christian Mehl, Volker Mehrmann, Hongguo Xu.
    Singular-value-like decomposition for complex matrix triples.
    J. Comput. Appl. Math., 233:1245-1276, 2010.
    pdf-file, Article: http://dx.doi.org/10.1016/j.cam.2008.02.017.
     
  32. Christian Mehl, Volker Mehrmann, Hongguo Xu.
    Structured decompositions for matrix triples: SVD-like concepts for structured matrices.
    Oper. Matrices, 3:303-356, 2009.
    pdf-file, Article: http://dx.doi.org/10.7153/oam-03-19.
     
  33. Christian Mehl, Volker Mehrmann, André C.M. Ran, Leiba Rodman.
    Perturbation analysis of Lagrangian invariant subspaces of symplectic matrices.
    Linear and Multilinear Algebra, 57:141-184, 2009.
    pdf-file, Article: http://dx.doi.org/10.1080/03081080701452508.
     
  34. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Numerical methods for palindromic eigenvalue problems: computing the anti-triangular Schur form.
    Numer. Linear Algebra Appl., 16:63-86, 2009.
    pdf-file (3.0M), Article: http://dx.doi.org/10.1002/nla.612.
     
  35. Christian Mehl.
    On asymptotic convergence of nonsymmetric Jacobi algorithms.
    SIAM J. Matrix Anal. Appl., 30: 291-311, 2008.
    pdf-file, Article: http://dx.doi.org/10.1137/060663246.
     
  36. Christian Mehl, Carsten Trunk.
    Normal matrices in degenerate indefinite inner product spaces.
    Oper. Theory Adv. Appl., 175: 193-209, 2007.
    pdf-file, Article: http://dx.doi.org/10.1007/978-3-7643-8270-4_11.
     
  37. Christian Mehl, André C.M. Ran, Leiba Rodman.
    Extension to maximal semidefinite invariant subspaces for hyponormal matrices in indefinite inner products.
    Linear Algebra Appl., 421: 110-116, 2007.
    pdf-file, Article: http://dx.doi.org/10.1016/j.laa.2006.05.007.
     
  38. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Structured polynomial eigenvalue problems: good vibrations from good linearizations.
    SIAM J. Matrix Anal. Appl., 28: 1029-1051, 2006.
    pdf-file, Article: http://dx.doi.org/10.1137/050628362.
     
  39. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Vector spaces of linearizations for matrix polynomials.
    SIAM J. Matrix Anal. Appl., 28: 971-1004, 2006.
    pdf-file, Article: http://dx.doi.org/10.1137/050628350.
     
  40. Christian Mehl, André C.M. Ran, Leiba Rodman.
    Invariant maximal positive subspaces and polar decompositions.
    Integral Equations Operator Theory, 56: 83-91, 2006.
    pdf-file, Article: http://dx.doi.org/10.1007/s00020-005-1407-z.
     
  41. Christian Mehl.
    Essential decomposition of normal matrices in real indefinite inner product spaces.
    Electron. J. Linear Algebra, 15: 84-106, 2006.
    pdf-file, Article: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol15_pp84-106.pdf.
     
  42. Christian Mehl.
    On classification of normal matrices in indefinite inner product spaces.
    Electron. J. Linear Algebra, 15: 50-83, 2006.
    pdf-file, Article: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol15_pp50-83.pdf.
     
  43. Christian Mehl, André C.M. Ran, Leiba Rodman.
    Polar decompositions of normal operators in indefinite inner product spaces.
    Oper. Theory Adv. Appl., 162: 277-292, 2006.
    pdf-file, Article: http://dx.doi.org/10.1007/3-7643-7453-5_15.
     
  44. Christian Mehl, André C.M. Ran, Leiba Rodman.
    Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products.
    Electron. J. Linear Algebra, 11: 192-204, 2004.
    pdf-file, Article: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol11_pp192-204.pdf.
     
  45. Christian Mehl, André C.M. Ran, Leiba Rodman.
    Semidefinite invariant subspaces: degenerate inner products.
    Oper. Theory Adv. Appl., 149: 467-486, 2004.
    pdf-file, Article: http://dx.doi.org/10.1007/978-3-0348-7881-4_19.
     
  46. Christian Mehl.
    Jacobi-like algorithms for the indefinite generalized Hermitian eigenvalue problem.
    SIAM J. Matrix Anal. Appl., 25: 964-985, 2004.
    pdf-file, Article: http://dx.doi.org/10.1137/S089547980240947X.
     
  47. Christian Mehl, Volker Mehrmann, Hongguo Xu.
    On doubly structured matrices and pencils that arise in linear response theory.
    Linear Algebra Appl., 380: 3-51, 2004.
    pdf-file, Article: http://dx.doi.org/10.1016/S0024-3795(02)00455-X.
     
  48. Christian Mehl, Leiba Rodman.
    Symmetric matrices with respect to sesquilinear forms.
    Linear Algebra Appl., 349: 55-75, 2002.
    pdf-file, Article: http://dx.doi.org/10.1016/S0024-3795(01)00598-5.
     
  49. Vladimir Bolotnikov, Chi-Kwong Li, Patrick Meade, Christian Mehl, Leiba Rodman.
    Shells of matrices in indefinite inner product spaces.
    Electron. J. Linear Algebra, 9: 67-92, 2002.
    pdf-file, Article: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol9_pp67-92.pdf.
     
  50. Christian Mehl, Leiba Rodman.
    Classes of normal matrices in indefinite inner products.
    Linear Algebra Appl., 336: 71-98, 2001.
    pdf-file, Article: http://dx.doi.org/10.1016/S0024-3795(01)00299-3.
     
  51. Brian Lins, Patrick Meade, Christian Mehl, Leiba Rodman.
    Normal matrices and polar decompositions in indefinite inner products.
    Linear and Multilinear Algebra, 49: 45-89, 2001.
    pdf-file, Article: http://dx.doi.org/10.1080/03081080108818685.
     
  52. Christian Mehl, Volker Mehrmann, Hongguo Xu.
    Canonical forms for doubly structured matrices and pencils.
    Electron. J. Linear Algebra, 7: 112-151, 2000.
    pdf-file, Article: http://www.math.technion.ac.il/iic/ela/ela-articles/articles/vol7_pp112-151.pdf.
     
  53. Christian Mehl.
    Anti-triangular and anti-m-Hessenberg forms for Hermitian matrices and pencils.
    Linear Algebra Appl., 317: 143-176, 2000.
    pdf-file, Article: http://dx.doi.org/10.1016/S0024-3795(00)00156-7.
     
  54. Christian Mehl.
    Condensed forms for skew-Hamiltonian/Hamiltonian pencils.
    SIAM J. Matrix Anal. Appl., 21: 454-476, 1999.
    pdf-file, Article: http://dx.doi.org/10.1137/S0895479898336513.
     
  55. Gregory Ammar, Christian Mehl, Volker Mehrmann.
    Schur-like forms for matrix Lie groups, Lie algebras and Jordan algebras.
    Linear Algebra Appl., 287: 11-39, 1999.
    pdf-file, Article: http://dx.doi.org/10.1016/S0024-3795(98)10133-7.
 
Books:
 
  1. Christian Mehl.
    Compatible Lie and Jordan algebras and applications to structured matrices and pencils.
    Logos, Berlin, 1999. ISBN 978-3-89722-173-4.
     
  2. Steffen Börm, Christian Mehl.
    Numerical Methods for Eigenvalue Problems.
    De Gruyter, Berlin, 2012. ISBN 978-3-11-025033-6.
 
Book Chapters:
 
  1. Christian Mehl, Hongguo Xu.
    Canonical forms of structured matrices and pencils.
    In: Numerical Algebra, Matrix Theory, Differential Algebraic Equations and Control Theory. Festschrift in Honor of Volker Mehrmann. Edited by Peter Benner, Matthias Bollhöfer, Daniel Kressner, Christian Mehl, Tatjana Stykel.
    Springer, Cham Heidelberg New York Dordrecht London, 2015, pp. 131-159. ISBN 978-3-319-15259-2.
    pdf-file (212k). Article: http://dx.doi.org/10.1007/978-3-319-15260-8_6
     
  2. Christian Mehl.
    Finite dimensional inner product spaces and applications in Numerical Analysis.
    In: Operator Theory. Edited by Daniel Alpay.
    Springer Basel, Basel, 2015, pp. 431-449. ISBN 978-3-0348-0666-4.
    pdf-file (957k). Article: http://dx.doi.org/10.1007/978-3-0348-0692-3_34-1
     
  3. Jörg Liesen, Christian Mehl.
    Matrix polynomials.
    In: Handbook of Linear Algebra 2nd Edition. Edited by Leslie Hogben.
    Discrete Mathematics and its Applications. Chapman & Hall/CRC, Boca Raton, 2013, pp. 18/1-18/18. ISBN 978-1-46-650728-9.
 
Other Publications: (This list only contains items that have not been published elsewhere.)
 
  1. Brian Lins, Patrick Meade, Christian Mehl, Leiba Rodman.
    Polar decompositions of indecomposable normal matrices in indefinite inner products: Explicit formulas and open problems.
    Preprint 2000-9, Fakultät für Mathematik, Technische Universität Chemnitz.
    pdf-file (261k).
     
  2. Brian Lins, Patrick Meade, Christian Mehl, Leiba Rodman.
    Research Problem: Indefinite inner product normal matrices,
    Linear and Multilinear Algebra, 49: 261-268, 2001.
    pdf-file (111k).
     
  3. Andreas Hilliges, Christian Mehl, Volker Mehrmann.
    On the solution of palindromic eigenvalue problems.
    Proceedings of the European Congress on Computational Methods in Applied Sciences and Engeneering (ECCOMAS), Jyväskylä, 24.7.-28.7.2004.
    Article.
     
  4. D. Steven Mackey, Niloufer Mackey, Christian Mehl, Volker Mehrmann.
    Palindromic polynomial eigenvalue problems: good vibrations from good linearizations.
    Technical Report No. 239, DFG Research Center Matheon, Berlin, 2006.
    pdf-file (294k).
 
Theses:
 
  1. Christian Mehl.
    Kompakte Hausdorffräume und ihre finalen Hüllen in Kategorien von Präkonvergenzräumen.
    Diplomarbeit, Universität Bielefeld, 1994.
     
  2. Christian Mehl.
    Compatible Lie and Jordan algebras and applications to structured matrices and pencils.
    Dissertation, Technische Universität Chemnitz, 1998.
     
  3. Christian Mehl.
    Eigenvalue problems that are structured with respect to indefinite inner products.
    Cumulative Habilitation thesis, Technische Universität Berlin, 2003.
Christian Mehl, 25.06.2024 Back to the Homepage