A block Newton method for nonlinear eigenvalue problems

Numerische Mathematik

Volumn 114, Issue 2, 2009, Pages 355-372

  Kressner, Daniel ^a  

^a Seminar für Angewandte Mathematik ^*  (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 76049115242     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-009-0259-x     Document Type: Article

References (31)

1. Absil P.-A., Mahony R., Sepulchre R., van Dooren P.: A Grassmann-Rayleigh quotient iteration for computing invariant subspaces. SIAM Rev. 44(1), 57-73 (2002).
2. Bai, Z., Demmel, J. W., Dongarra, J. J., Ruhe, A., van der Vorst, H (ed.).: Templates for the Solution of Algebraic Eigenvalue Problems: Software, Environments, and Tools. SIAM, Philadelphia (2000).
3. Benzi M., Golub G. H., Liesen J.: Numerical solution of saddle point problems. Acta Numer. 14, 1-137 (2005).
4. Betcke M., Voss H.: Stationary Schrödinger equations governing electronic states of quantum dots in the presence of spin-orbit splitting. Appl. Math. 52(3), 267-284 (2007).
5. Betcke M. M., Voss H.: Restarting projection methods for rational eigenproblems arising in fluid-solid vibrations. Math. Model. Anal. 13(2), 171-182 (2008).
6. Betcke, T., Kressner, D.: Perturbation, computation and refinement of invariant pairs for matrix polynomials. Technical report 2009-21, seminar for applied mathematics, ETH Zurich, July 2009.
7. Betcke T., Voss H.: A Jacobi-Davidson type projection method for nonlinear eigenvalue problems. Future Gener. Comput. Syst. 20, 363-372 (2004).
8. Beyn, W.-J., Kleß, W., Thümmler, V.: Continuation of low-dimensional invariant subspaces in dynamical systems of large dimension. In: Ergodic theory, analysis, and efficient simulation of dynamical systems, pp. 47-72. Springer, Berlin (2001).
9. Beyn, W.-J., Thümmler, V.: Continuation of invariant subspaces for parameterized quadratic eigenvalue problems. Technical report, University of Bielefeld, Department of Mathematics (2008).
10. Chatelin, F.: Simultaneous Newton's iteration for the eigenproblem. In: Defect correction methods (Oberwolfach, 1983), volume 5 of Comput. Suppl., pp. 67-74. Springer, Vienna (1984).
11. Demmel J. W.: Three methods for refining estimates of invariant subspaces. Computing 38, 43-57 (1987).
12. Dennis J. E. Jr, Traub J. F., Weber R. P.: The algebraic theory of matrix polynomials. SIAM J. Numer. Anal. 13(6), 831-845 (1976).
13. Gaier D.: Vorlesungen über Approximation im Komplexen. Birkhäuser Verlag, Basel (1980).
14. Gohberg, I., Lancaster, P., Rodman, L.: Matrix Polynomials. Academic Press. [Harcourt Brace Jovanovich Publishers], New York, Computer Science and Applied Mathematics (1982).
15. Green K., Wagenknecht T.: Pseudospectra and delay differential equations. J. Comput. Appl. Math. 196(2), 567-578 (2006).
16. Higham, N. J.: Functions of Matrices. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2008).
17. Krantz S. G.: Function Theory of Several Complex Variables. Wiley, New York (1982).
18. Mathias R.: A chain rule for matrix functions and applications. SIAM J. Matrix Anal. Appl. 17(3), 610-620 (1996).
19. Meerbergen K.: Locking and restarting quadratic eigenvalue solvers. SIAM J. Sci. Comput. 22(5), 1814-1839 (2000).
20. Mehrmann, V., Voss, H.: Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods. GAMM Mitteilungen 27 (2004).
21. Michiels, W., Niculescu, S.-I.: Stability and Stabilization of Time-delay Systems, vol. 12 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2007).
22. Najfeld I., Havel T. F.: Derivatives of the matrix exponential and their computation. Adv. Appl. Math. 16, 321-375 (1995).
23. Sleijpen G. L. G., Booten A. G. L., Fokkema D. R., van der Vorst H. A.: Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems. BIT 36(3), 595-633 (1996).
24. Solovev S. I.: Preconditioned iterative methods for a class of nonlinear eigenvalue problems. Linear Algebra Appl. 415(1), 210-229 (2006).
25. Stewart G. W., Sun J.-G.: Matrix Perturbation Theory. Academic Press, New York (1990).
26. Voss H.: A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration. Appl. Math. 48(6), 607-622 (2003).
27. Voss H.: An Arnoldi method for nonlinear eigenvalue problems. BIT 44(2), 387-401 (2004).
28. Voss, H.: A Jacobi-Davidson method for nonlinear eigenproblems. In: Computational Science-ICCS 2004. Part II, vol. 3037 of Lecture Notes in Computer Science, pp. 34-41. Springer, Berlin (2004).
29. Voss H.: Iterative projection methods for computing relevant energy states of a quantum dot. J. Comput. Phys. 217(2), 824-833 (2006).
30. Voss H.: A Jacobi-Davidson method for nonlinear and nonsymmetric eigenproblems. Comput. Struct. 85(17/18), 1284-1292 (2007).
31. Voss H., Werner B.: A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems. Math. Methods Appl. Sci. 4(3), 415-424 (1982).