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RESEARCH PAPERS: Mechanisms and Robotics Papers

Using Chaos to Obtain Global Solutions in Computational Kinematics

[+] Author and Article Information
V. T. Jovanovic

T. Sendzimir, Inc. Waterbury, CT 06721

K. Kazerounian

Dept. of Mech. Eng., University of Connecticut, Storrs, CT 06269-3139

J. Mech. Des 120(2), 299-304 (Jun 01, 1998) (6 pages) doi:10.1115/1.2826972 History: Received February 01, 1997; Online December 11, 2007

Abstract

In this paper we examine the sensitive dependence on the initial conditions of the Newton-Raphson search technique. It is demonstrated that this sensitivity has a fractal nature which can be effectively utilized to find all solutions to a nonlinear equation. The developed technique uses an important feature of fractals to preserve shape of basins of attraction on infinitely small scales.

Copyright © 1998 by The American Society of Mechanical Engineers
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