×

zbMATH — the first resource for mathematics

Chaotic descent method and fractal conjecture. (English) Zbl 0983.74080
From the summary: We attempt to utilize computational instabilities in solving systems of nonlinear equations and optimization theory that results in development of a new method, chaotic descent. The method is based on descending to global minima via regions that are the source of computational chaos. Also, we present a fractal conjecture that in the future might lead towards direct solving of systems of nonlinear equations.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
74P99 Optimization problems in solid mechanics
65K10 Numerical optimization and variational techniques
37N15 Dynamical systems in solid mechanics
28A80 Fractals
65H10 Numerical computation of solutions to systems of equations
PDF BibTeX Cite
Full Text: DOI
References:
[1] et al. Iterative Methods for Nonlinear Optimization Problems. Prentice-Hall: Englewood Cliffs, NJ, 1972.
[2] Globally Optimal Design. Wiley: New York, 1978.
[3] Jovanovic, International Journal for Numerical Methods in Engineering 42 pp 729– (1998)
[4] Julia, Journal de Mathematiques Pureset Appliques 8 pp 47– (1918)
[5] Cayley, American Journal of Mathematics pp 97– (1879)
[6] et al. Chaos and Fractals: New Frontiers of Science. Springer: New York, 1992. · Zbl 0779.58004
[7] Functions of One Complex Variable. Springer: New York, 1978.
[8] An Introduction to Chaotic Dynamical System. Perseus Publishing Co., a division of Harper/Colins: Reading, 1989.
[9] Identifying, utilizing and improving chaotic numerical instabilities in computational kinematics. Ph.D. Thesis; The University of Connecticut, 1997.
[10] Jovanovic, ASME Journal of Mechanical Design 120 pp 299– (1998)
[11] Fatou, Bulletin of the Society of Mathematics of France 47 pp 161– (1919)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.