A general view of minimally extended systems for simple bifurcation points

ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik

Volumn 77, Issue 2, 1997, Pages 83-97

  Allgower, E L ^a   Schwetlick, H ^b  

^a Veterinary Dentistry and Oral Surgery   (United States)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444446076     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.19970770203     Document Type: Review

References (14)

1. ALLGOWER, E. L.; GEORG, K.: Numerical continuation methods: An introduction. Springer, Berlin 1990.
2. ALLGOWER, E. L.; SCHWETLICK, H.: Stable computation of simple bifurcation points and emanating branches. Lecture, held at the Conference "Computational methods for nonlinear phenomena", January 1993, Oberwolfach, Germany 1993.
3. GOLUB, G. H.; VAN LOAN, C. F.: Matrix computations. 2nd ed. Johns Hopkins University Press, Baltimore-London 1989.
4. GRIEWANK, A.; GORLISS, G. (eds.): Automatic differentiation of algorithms: Theory, implementation, and application. SIAM, Philadelphia 1991.
5. GRIEWANK, A.; REDDIEN, G. W.: Characterization and computation of generalized turning points. SIAM J. Numer. Anal. 21 (1984), 176-185.
6. _: Computation of cusp singularities of operator equations and their discretizations. J. Computat. Appl. Math. 26 (1989), 133-153.
7. JANOVSKY, V.: A note on computing simple bifurcation points. Computing 43 (1989), 27-36.
8. MOORE, G.; SPENCE, A.: The calculation of turning points of nonlinear equations. SIAM J. Numer. Anal. 17 (1980), 567-576.
9. PÖNISCH, G.: Computing simple bifurcation points using a minimally extended system of nonlinear equations. Computing 35 (1985), 277-294.
10. PÖNISCH, G.; SCHWETLICK, H.: Computing turning points of curves implicitly defined by nonlinear equations depending on a parameter. Computing 26 (1981), 107-121.
11. REINSCHKE, K.: Personal communication to A. GRIEWANK 1995.
12. RHEINBOLDT, W. C.: Numerical analysis of parametrized nonlinear equations. J. Wiley, New York 1986.
13. SEYDEL, R.: Numerical computation of branch points of nonlinear equations. Numer. Math. 33 (1979), 339-352.
14. WEBER, H.: On the numerical solution of some finite-dimensional bifurcation problems. Numer. Funct. Anal. Optim. 3 (1981), 341-366.