Due
to the fact
that numerical linear algebra
appears in a wide variety of fields,
it has an unusual role as
a very interdisciplinary subject
and
my research has involved topics
in a number of related fields, such as
systems and control, quantum mechanics, optimization and
some applications in mechanical engineering.

Example of description of convergence as a function of a parameter for two choices of the Rayleigh-quotient vectors (E. Jarlebring and W. Michiels,

Example of a solution to the Gross-Pitaevskii equation computed with the iterative method in E. Jarlebring, S. Kvaal and W. Michiels,

Related publications:

- R. Van Beeumen, E. Jarlebring and W. Michiels
*A rank-exploiting infinite Arnoldi algorithm for nonlinear eigenvalue problems*

Numer. Linear Algebra Appl., 23(4):607-628, 2016 - E. Jarlebring, S. Kvaal and W. Michiels
*An inverse iteration method for eigenvalue problems with eigenvector nonlinearities*

SIAM J. Sci. Comput., 36-4:A1978-A2001, 2014 - E. Jarlebring, K. Meerbergen and W. Michiels
*Computing a partial Schur factorization of nonlinear eigenvalue problems using the infinite Arnoldi method*

SIAM J. Matrix Anal. Appl., 35(2):411-436, 2014 - E. Jarlebring, W. Michiels and K. Meerbergen
*A linear eigenvalue algorithm for the nonlinear eigenvalue problem*

Numerische Mathematik, 122(1):169-195, 2012 - E. Jarlebring and W. Michiels
*Analyzing the convergence factor of residual inverse iteration*

BIT numerical mathematics, 51(4):937-957, 2011 - E. Jarlebring, K. Meerbergen and W. Michiels
*A Krylov method for the delay eigenvalue problem*

SIAM J. Sci. Comput., 32(6):3278-3300, 2010 - E. Jarlebring
*Convergence factors of Newton methods for nonlinear eigenvalue problems*

Linear Algebra Appl., 436:3943-3953, 2012 - E. Jarlebring and H. Voss
*Rational Krylov for Nonlinear Eigenproblems, an Iterative Projection Method*

Applications of Mathematics, 50(6):543-554, 2005

- Compute eigenvalues which are solutions to a nonlinear eigenvalue problem
- Computing and characterize stability by computing conditions such that there is an imaginary eigenvalue
- Compute the ℋ₂ norm of a time-delay systems
- Stability of a machine-tool milling model
- Model reduction techniques for time-delay systems based on balanced truncation, dominant pole selection and moment matching

Example of description of stability with manually computed eigenvalues and the expansion from theory with an application from machine tool milling:

Related publications:

- E. Jarlebring, T. Damm and W. Michiels
*Model reduction of time-delay systems using position balancing and delay Lyapunov equations*

Mathematics of Control, Signals, and Systems, 25(2):147-166, 2013 - M. Saadvandi, K. Meerbergen and E. Jarlebring
*On dominant poles and model reduction of second order time-delay systems*

Appl. Numer. Math., 62(1):21-34, 2012 - J. Vanbiervliet, W. Michiels and E. Jarlebring
*Using spectral discretization for the optimal ℋ₂ design of time-delay systems*

Int. J. Control, 84(2):228-241, 2011 - E. Jarlebring, J. Vanbiervliet and W. Michiels
*Characterizing and computing the ℋ₂ norm of time-delay systems by solving the delay Lyapunov equation*

IEEE Trans. Autom. Control, full paper, 56(4):814-825, 2011 - W. Michiels, E. Jarlebring and K. Meerbergen
*Krylov-based model order reduction of time-delay systems*

SIAM J. Matrix Anal. Appl., 32(4):1399-1421, 2011 - E. Jarlebring, W. Michiels, K. Meerbergen
*The infinite Arnoldi method and an application to time-delay systems with distributed delays*

chapter in edited volume, in In R. Sipahi, T. Vyhlidal, P. Pepe, S.-I. Niculescu, Eds., 'Time Delay Systems - Methods, Applications and New Trends' - E. Jarlebring, K. Meerbergen and W. Michiels
*A Krylov method for the delay eigenvalue problem*

SIAM J. Sci. Comput., 32(6):3278-3300, 2010 - E. Jarlebring and W. Michiels
*Invariance properties in the root sensitivity of time-delay systems with double imaginary roots*

Automatica, 46:1112-1115, 2010 - E. Jarlebring
*Critical delays and Polynomial Eigenvalue Problems*

J. Comput. Appl. Math., 224(1):296-306, 2009 - E. Jarlebring and T. Damm
*The Lambert W function and the spectrum of some multidimensional time-delay systems*

Automatica, 43(12):2124-2128, 2007 - E. Jarlebring

*The spectrum of delay-differential equations: numerical methods, stability and perturbation.*

PhD thesis, Inst. Comp. Math, TU Braunschweig, 2008

Related publications:

- E. Jarlebring, S. Kvaal and W. Michiels
*Computing all pairs (λ,μ) such that λ is a double eigenvalue of A+μB*

SIAM J. Matrix Anal. Appl., 32(3):902-927, 2011 - S. Kvaal, E. Jarlebring and W. Michiels
*Computing singularities of perturbation series*

Phys. Rev. A, 83:032505, 2011 - E. Jarlebring and W. Michiels
*Invariance properties in the root sensitivity of time-delay systems with double imaginary roots*

Automatica, 46:1112-1115, 2010 - E. Jarlebring and M.E. Hochstenbach
*Polynomial two-parameter eigenvalue problems and matrix pencil methods for stability of delay-differential equations*

Linear Algebra Appl., 431(3-4):369-380, 2009