Abstract
Large and sparse rational eigenproblems where the rational term is of low rank k arise in vibrations of fluid–solid structures and of plates with elastically attached loads. Exploiting model order reduction techniques, namely the Padé approximation via block Lanczos method, problems of this type can be reduced to k–dimensional rational eigenproblems which can be solved efficiently by safeguarded iteration.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bai, Z., Freund, R.W.: A symmetric band Lanczos process based on coupled recurrences and some applications. SIAM J. Sci. Comput. 23, 542–562 (2001)
Betcke, T., Voss, H.: A Jacobi–Davidson–type projection method for nonlinear eigenvalue problems. Future Generation Computer Systems 20(3), 363–372 (2004)
Conca, C., Planchard, J., Vanninathan, M.: Fluid and Periodic Structures. Research in Applied Mathematics, vol. 24. Masson, Paris (1995)
Feldmann, P., Freund, R.W.: Efficient linear circuit analysis by Padé approximation via the Lanczos process. In: Proceedings of EURO-DAC 1994 with EURO-VHDL 1994, pp. 170–175. IEEE Computer Society Press, Los Alamitos (1994)
Freund, R.W.: Computation ofmatrix Padé approximations of transfer functions via a Lanczostype process. In: Chui, C., Schumaker, L. (eds.) Approximation Theory VIII. Approximation and Interpolation, vol. 1, pp. 215–222. World Scientific Publishing Co., Singapore (1995)
Rogers, E.H.: A minmax theory for overdamped systems. Arch. Rat. Mech. Anal. 16, 89–96 (1964)
Voss, H.: Initializing iterative projection methods for rational symmetric eigenproblems. In: Online Proceedings of the Dagstuhl Seminar Theoretical and Computational Aspects of Matrix Algorithms, Schloss Dagstuhl (2003), ftp://ftp.dagstuhl.de
Voss, H.: A rational spectral problem in fluid–solid vibration. Electronic Transactions on Numerical Analysis 16, 94–106 (2003)
Voss, H.: An Arnoldi method for nonlinear eigenvalue problems. BIT Numerical Mathematics 44, 387–401 (2004)
Voss, H., Werner, B.: A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems. Math. Meth. Appl. Sci. 4, 415–424 (1982)
Voss, H., Werner, B.: Solving sparse nonlinear eigenvalue problems. Technical Report 82/4, Inst. f. Angew. Mathematik, Universität Hamburg (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blömeling, F., Voss, H. (2006). A Model-Order Reduction Technique for Low Rank Rational Perturbations of Linear Eigenproblems. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_35
Download citation
DOI: https://doi.org/10.1007/11558958_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29067-4
Online ISBN: 978-3-540-33498-9
eBook Packages: Computer ScienceComputer Science (R0)