Abstract
The convergence of the method of steepest descent can be studied with computer graphics. The number of iterations required for convergence and the basin of attraction determined by the algorithm are both sensitive to initial conditions. The convergence in valleys is studied and beautiful, chaotic, images of the convergence are given.
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References
Barnsley M (1988) Fractals everywhere. Academic Press, New York
Cooper L, Steinberg D (1970) Introduction to methods of optimization. W.B. Saunders, Philadelphia
Dahlquist G, Bjorck A, Anderson N (1974) Numerical methods. Prentice Hall, Engelwood Cliffs, New Jersey
Locascio A, Burns SA (1990) Graphical Characterization of diverse design optimization processes. General Engineering Report No. 90-06, Engineering Documents Center No. UILU-ENG-90-3029, Univ. of Illinios at Urbana-Champaign
Mandelbrot B (1982) The fractal geometry of nature. Freeman, New York
Motyka MA, Reiter CA (1990) Chaos and Newton's method on systems Comput Graph 14:131–134
Peitgen H-O, Saupe D, Haeseler FV (1984) Cayley's problem and Julia sets. Math Intellig 6:11–20
Pickover CA (1990) Computers, pattern, chaos and beauty. St. Martin's Press, New York
Powell MJD (1964) An efficient algorithm for finding the minimum of a function of several variables without calculating derivatives. Comput J 7:155–162
Walsh GR (1975) Methods of optimization. John-Wiley, New York
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Reiter, C.A. Visualizing steepest descent. The Visual Computer 8, 64–67 (1991). https://doi.org/10.1007/BF01900846
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DOI: https://doi.org/10.1007/BF01900846