| Title:
|
Continuation of invariant subspaces via the Recursive Projection Method (English) |
| Author:
|
Janovský, V. |
| Author:
|
Liberda, O. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
2003 |
| Pages:
|
241-255 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The Recursive Projection Method is a technique for continuation of both the steady states and the dominant invariant subspaces. In this paper a modified version of the RPM called projected RPM is proposed. The modification underlines the stabilization effect. In order to improve the poor update of the unstable invariant subspace we have applied subspace iterations preconditioned by Cayley transform. A statement concerning the local convergence of the resulting method is proved. Results of numerical tests are presented. (English) |
| Keyword:
|
steady states |
| Keyword:
|
pathfollowing |
| Keyword:
|
stability exchange |
| Keyword:
|
unstable invariant subspace |
| MSC:
|
47H17 |
| MSC:
|
47J25 |
| MSC:
|
65H17 |
| MSC:
|
65H20 |
| MSC:
|
65P30 |
| idZBL:
|
Zbl 1099.65046 |
| idMR:
|
MR1994376 |
| DOI:
|
10.1023/A:1026058514236 |
| . |
| Date available:
|
2009-09-22T18:13:53Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134531 |
| . |
| Reference:
|
[1] E. L. Allgower. K. Georg: Numerical Continuation Methods.Springer Verlag, New York, 1990. Zbl 0717.65030, MR 1059455 |
| Reference:
|
[2] J. Bošek, V. Janovský: A note on the recursive projection method. Proceedings of GAMM96.Z. Angew. Math. Mech. (1977), 437-440. |
| Reference:
|
[3] B. D. Davidson: Large-scale continuation and numerical bifurcation for partial differential equations.SIAM J. Numer. Anal. 34 (1997), 2001–2027. Zbl 0894.65023, MR 1472207 |
| Reference:
|
[4] T. J. Garratt, G. Moore and A. Spence: A generalised Cayley transform for the numerical detection of Hopf bifurcation points in large systems.Contributions in numerical mathematics, World Sci. Ser. Appl. Anal. (1993), 177–195. MR 1299759 |
| Reference:
|
[5] G. H. Golub, Ch. F. van Loan: Matrix Computations.The Johns Hopkins University Press, Baltimore, 1996. MR 1417720 |
| Reference:
|
[6] V. Janovský, O. Liberda: Recursive Projection Method for detecting bifurcation points.Proceedings SANM’99, Union of Czech Mathematicians and Physicists, 1999, pp. 121–124. |
| Reference:
|
[7] V. Janovský, O. Liberda: Projected version of the Recursive Projection Method algorithm.Proceedings of 3rd Scientific Colloquium, Institute of Chemical Technology, Prague, 2001, pp. 89–100. |
| Reference:
|
[8] M. Kubíček, M. Marek: Computational Methods in Bifurcation Theory and Dissipative Structures.Springer, 1983. MR 0719370 |
| Reference:
|
[9] J. Kurzweil: Ordinary Differential Equations.Elsevier, 1986. Zbl 0667.34002, MR 0929466 |
| Reference:
|
[10] K. Lust, D. Roose: Computation and bifurcation analysis of periodic solutions of large–scale systems.IMA Preprint Series #1536, Feb. 1998, IMA, University of Minnesota. MR 1768366 |
| Reference:
|
[11] G. M. Shroff, H. B. Keller: Stabilization of unstable procedures: the Recursive Projection Method.SIAM J. Numer. Anal. 30 (1993), 1099–1120. MR 1231329, 10.1137/0730057 |
| . |
