Continuation of invariant subspaces via the Recursive Projection Method

Vladimír Janovský; O. Liberda

Applications of Mathematics (2003)

  • Volume: 48, Issue: 4, page 241-255
  • ISSN: 0862-7940

Abstract

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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.

How to cite

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Janovský, Vladimír, and Liberda, O.. "Continuation of invariant subspaces via the Recursive Projection Method." Applications of Mathematics 48.4 (2003): 241-255. <http://eudml.org/doc/33148>.

@article{Janovský2003,
abstract = {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.},
author = {Janovský, Vladimír, Liberda, O.},
journal = {Applications of Mathematics},
keywords = {steady states; pathfollowing; stability exchange; unstable invariant subspace; steady states; pathfollowing; stability exchange; unstable invariant subspace},
language = {eng},
number = {4},
pages = {241-255},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuation of invariant subspaces via the Recursive Projection Method},
url = {http://eudml.org/doc/33148},
volume = {48},
year = {2003},
}

TY - JOUR
AU - Janovský, Vladimír
AU - Liberda, O.
TI - Continuation of invariant subspaces via the Recursive Projection Method
JO - Applications of Mathematics
PY - 2003
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 48
IS - 4
SP - 241
EP - 255
AB - 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.
LA - eng
KW - steady states; pathfollowing; stability exchange; unstable invariant subspace; steady states; pathfollowing; stability exchange; unstable invariant subspace
UR - http://eudml.org/doc/33148
ER -

References

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  2. A note on the recursive projection method. Proceedings of GAMM96, Z. Angew. Math. Mech. (1977), 437-440. (1977) 
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  4. 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. (1993) MR1299759
  5. Matrix Computations, The Johns Hopkins University Press, Baltimore, 1996. (1996) MR1417720
  6. Recursive Projection Method for detecting bifurcation points, Proceedings SANM’99, Union of Czech Mathematicians and Physicists, 1999, pp. 121–124. (1999) 
  7. Projected version of the Recursive Projection Method algorithm, Proceedings of 3rd Scientific Colloquium, Institute of Chemical Technology, Prague, 2001, pp. 89–100. (2001) 
  8. Computational Methods in Bifurcation Theory and Dissipative Structures, Springer, 1983. (1983) MR0719370
  9. Ordinary Differential Equations, Elsevier, 1986. (1986) Zbl0667.34002MR0929466
  10. Computation and bifurcation analysis of periodic solutions of large–scale systems, IMA Preprint Series #1536, Feb.  1998, IMA, University of Minnesota. MR1768366
  11. 10.1137/0730057, SIAM J.  Numer. Anal. 30 (1993), 1099–1120. (1993) MR1231329DOI10.1137/0730057

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