Convergence of Newton's Method via Lyapunov Analysis
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The convergence of Newton's method was demonstrated using Lyapunov's direct method. For points that begins near the solution x*, the Lyapunov function that led to the inequality condition was conservative. Examples of robot trajectories, where nine robots were tasked with localizing an unknown source were presented. Analysis shows that the stability of the equilibrium point along trajectories commensurate with the position update law for each robot, follows from the Lyapunov analysis convergence proof.
author list (cited authors)
Hurtado, J. E., & Robinett, R. D.