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EUROCAST
2005
Springer

Convergence of Iterations

14 years 4 months ago
Convergence of Iterations
Convergence is a central problem in both computer science and in population biology. Will a program terminate? Will a population go to an equilibrium? In general these questions are quite difficult – even unsolvable. In this paper we will concentrate on very simple iterations of the form xt+1 = f(xt) where each xt is simply a real number and f(x) is a reasonable real function with a single fixed point. For such a system, we say that an iteration is “globally stable” if it approaches the fixed point for all starting points. We will show that there is a simple method which assures global stability. Our method uses bounding of f(x) by a self-inverse function. We call this bounding “enveloping” and we show that enveloping implies global stability. For a number of standard population models, we show that local stability implies enveloping by a self-inverse linear fractional function and hence global stability. We close with some remarks on extensions and limitations of our metho...
Paul Cull
Added 27 Jun 2010
Updated 27 Jun 2010
Type Conference
Year 2005
Where EUROCAST
Authors Paul Cull
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