TL;DR
This paper introduces a matrix-based method for continuous iteration, enabling an order-to-order approach to tetration and proposing its potential significance in describing complex dynamical systems.
Contribution
It presents a novel matrix approach to continuous iteration, specifically for tetration, offering an algorithmic framework and new insights into dynamical systems.
Findings
Matrix approach facilitates continuous iteration of functions.
Algorithmic method for tetration is developed.
Potential applications in complex dynamical systems are suggested.
Abstract
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order approximations suggest that tetration may come to be of great interest for the description of involved dynamical systems.
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Taxonomy
TopicsNumerical methods for differential equations · Quantum chaos and dynamical systems · Matrix Theory and Algorithms