Karl Meerbergen
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Eigenvalue problems

Publications

  • K. Meerbergen, A. Spence, and D. Roose. Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices. BIT, 34:409--423, 1994.
  • K. Meerbergen and D. Roose. Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems. IMA J. Numer. Anal., 16:297--346, 1996.
  • K. Meerbergen and D. Roose. The restarted Arnoldi method applied to iterative linear system solvers for the computation of rightmost eigenvalues. SIAM J. Matrix Anal. Applic., 18:1--20, 1997.
  • K. Meerbergen and A. Spence. Implicitly restarted Arnoldi and purification for the shift-invert transformation. Math. Comp., 66:667--689, 1997.
  • G. De Samblanx, K. Meerbergen, and A. Bultheel. The implicit application of a rational filter in the RKS method. BIT, 37:925--947, 1997.
  • R.B. Lehoucq and K. Meerbergen. Using generalized Cayley transformations within an inexact rational Krylov sequence method. SIAM J. Matrix Anal. Applic., 20(1):131--148, 1998.
  • K. Meerbergen. A theoretical comparison between inner products in the shift-invert Arnoldi method and the spectral transformation Lanczos method. ETNA, 7:90--103, 1998.
  • K. Meerbergen and M. Sadkane. Using Krylov approximations to the matrix exponential operator in Davidson's method. Applied Numerical Mathematics, 31:331--351, 1999.
  • K. Meerbergen. Changing poles in the rational Lanczos method for the Hermitian eigenvalue problem. Num. Lin. Alg. Appl., 8:33-52, 2001.
  • K. Meerbergen. Locking and restarting quadratic eigenvalue solvers. SIAM. Sci. Comput., 22:1814--1839, 2001.
  • F. Tisseur and K. Meerbergen. The quadratic eigenvalue problem. SIAM Review, 43(2):235--286, 2001.
  • K. Meerbergen. The Lanczos method with semi-definite inner product. BIT, 41(5):1069--1078, 2001.
  • K. Meerbergen. The Quadratic Arnoldi method for the solution of the quadratic eigenvalue problem. SIAM J. Matrix Anal. Applic., 30(4):1463-1482, 2008.
  • K. Meerbergen and A. Spence. Shift-and-invert iteration for purely imaginary eigenvalues with application to the detection of Hopf Bifurcations in large scale problems. SIAM. J. Matrix Anal. Applic., 31(4):1982-1999, 2010.
  • E. Jarlebring, K. Meerbergen and W. Michiels. A Krylov method for the delay eigenvalue problem. SIAM J. Scientific Computing, 32(6):3278-3300, 2010.
  • K. Meerbergen and R. Vandebril. A reflection on the implicitly restarted Arnoldi method for computing eigenvalues near a vertical line. Linear Algebra and its Applications, 436(8) (Special Issue for Danny Sorensen), pages 2828-2844, 2012.
  • H. Elman, K. Meerbergen, A. Spence and M. Wu. Lyapunov inverse iteration for identifying Hopf bifurcations in models of incompressible flow. SIAM Journal Scientific Computing, Accepted for publication.
  • K. Meerbergen, C. Schröder and H. Voss. A Jacobi-Davidson method for two real parameter nonlinear eigenvalue problems arising from delay differential equations, Numerical Linear Algebra with Applications, Accepted for publication.

Edited volumes

  • R.B. Morgan and K. Meerbergen. Inexact Methods and Preconditioning. In Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide, Z. Bai, J. Demmel, J. Dongarra, A. Ruhe and H. van der Vorst, editors. SIAM, Philadelphia, USA, 2000.

Proceedings papers

  • K. Meerbergen and D. Roose. Finding eigenvalues to the right of a given line. In P.S. Vassilevski and S.D. Margenov, editors, Second IMACS Symposium on Iterative Methods in Linear Algebra, Volume 3 of IMACS Series in Computational and Applied Mathematics, pages 402--412, Dept. of Computer Science, Rutgers University, Piscataway, NJ 08855, 1996. IMACS.
  • J. De Vlieger and K. Meerbergen. Analysis and Computation of Eigenvalues of Symmetric Fuzzy Matrices. AIP Conference Proceedings, 1168(1) pp. 278-281, 2009
  • E. Jarlebring, K. Meerbergen and W. Michiels. An Arnoldi method with structured starting vectors for the delay eigenvalue problem. IFAC TDS 2010. Accepted for publication.

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