Chaotic descent method and fractal conjecture

International Journal for Numerical Methods in Engineering

Volumn 48, Issue 1, 2000, Pages 137-152

  Jovanovic, Vojin ^a  

^a STEVENS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Chaos; Fractals; Newton Raphson; Non linear equations; Optimization

Indexed keywords

COMPUTATIONAL METHODS; FRACTURE MECHANICS; NONLINEAR EQUATIONS; NONLINEAR SYSTEMS; OPTIMIZATION; RANDOM PROCESSES;

CHAOTIC DESCENT METHODS; FRACTAL CONJECTURE; NEWTON-RAPHSON METHODS;

CHAOS THEORY;

EID: 0034186863     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(20000510)48:1<137::AID-NME876>3.0.CO;2-X     Document Type: Article

References (11)

1. Jacoby SL et al. Iterative Methods for Nonlinear Optimization Problems. Prentice-Hall: Englewood Cliffs, NJ, 1972.
2. Wilde DJ. Globally Optimal Design. Wiley: New York, 1978.
3. Jovanovic VT, Kazerounian K. On the metrics and coordinate-system-induced sensitivity. International Journal for Numerical Methods in Engineering 1998; 42(4):729-747.
4. Julia G. Memoire sur l'iteration des fonctions rationelles. Journal de Mathematiques Pureset Appliques 1918; 8:47-245.
5. Cayley A. The Newton-Fourier imaginary problem. American Journal of Mathematics, 1879; 97.
6. Peitgen H et al. Chaos and Fractals: New Frontiers of Science. Springer: New York, 1992.
7. Conway JB. Functions of One Complex Variable. Springer: New York, 1978.
8. Devaney RL. An Introduction to Chaotic Dynamical System. Perseus Publishing Co., a division of Harper/Colins: Reading, 1989.
9. Jovanovic V. Identifying, utilizing and improving chaotic numerical instabilities in computational kinematics. Ph.D. Thesis; The University of Connecticut, 1997.
10. Jovanovic VT, Kazerounian K. Using chaos to obtain global solutions in computational kinematics. ASME Journal of Mechanical Design 1998; 120(2):299-304.
11. Fatou MP. Sur les equations fonctionelles. Bulletin of the Society of Mathematics of France 1919; 47:161-271.