## A Dynamical Systems Approach to the Polygonal
Approximation of Plane Convex Compacts

### Petar S. Kenderov and Nikolai K. Kirov

Key words: polygonal approximation of plane convex sets,
dynamical systems,
global optimization,
variable knots spline approximation.
### Abstract

A connection is described between the polygonal approximation of a
compact convex set in R^2 and some dynamical systems on
the unit circumference in R^2. Basing on this a numerical procedure
is proposed for finding a best approximating n-gon for an arbitrary
compact convex set in R^2 (w.r.t. Hausdorff metric). The algorithm
provides a solution to
a specific global optimization problem where the function to be
minimized has more than one local minimum. In one of its
equivalent formulations the above approximation problem
can be considered as a specific spline approximation problem. From
this point of view our algorithm provides also a solution
to a specific variable knots spline approximation problem.

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